Trigonometry And Special Right Triangles Test

Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. This quiz/worksheet will emphasize the Pythagorean Theorem's factors and trigonometry. Decide whether the numbers can represent the side lengths of a triangle. In case you need them, here are the Trig Triangle Formula Tables, the Triangle Angle Calculator is also available for angle only calculations. Create a right angle triangle with angles of 30, 60, and 90 degrees. Explaining How to find the missing sides of right triangles using the relationships of sides for 30-60-90 right triangles, 45-45-90 right triangles, and 3-4-5 right triangles. Using Trig to Find a Missing Angle of a Right Triangle - Explanation, Examples, and Practice Problems  Explanation of Trig Functions with Interactive Visual Guide; Trigonometry Explained by the Unit Circle Quadrants; Inverse Trig Practice Quiz; Trig Ratios Practice Quiz; Reciprocal Trig Functions Explanations and Example Problems. Discovery of Special Triangles. You don’t necessarily have to know them off the top of your head, but it could potentially save you a lot of time, so it’s worth taking a look at. Similiarity and the Angle-Angle Criterion HSG-SRT. Right triangles have some unique qualities. State if each triangle is acute, obtuse, or right. The three most common trigonometric ratios are sine, cosine, and tangent, abbreviated sin, cos, and tan. Displaying all worksheets related to - Right Triangles Trigonometry. Homework/Answers. involving right triangles using the Pythagorean Theorem. S t hAPlJlR sryi_gYhntssG trIe[sKebrGvWeNdg. 14 Gina Wilson (AB Things Algebn),. Test Ch 9 Right Triangle Test. Students who took this test also took :. Please do not copy or share the Answer Keys or other subscriber content. On this page you can read or download unit 8 test study guide right triangles trigonometry in PDF format. Using the Pythagorean Theorem. Site map; Special right triangles test. You also need to be able to use them to find the length of any side of a right triangle in terms of any other side and one of the angles. One pair is anchored to the ground at 45 degree angles, the other pair is anchored at 60 degree angles. In this video I take you through the basics of working with special right triangles in Geometry. It can be used as a Quiz or adapted as Classwork, Homework, or Extra Credit. Opening – Warm-up: √50 + √32. 5 Law of Sines and Cosines 8. For more information on how I plan to implement these quick quizzes, check out this video Special Right Triangles quick quiz closure. There is also a perpendicular from one vertex. Algebra2/Trig Chapter 9 Packet In this unit, students will be able to: Use the Pythagorean theorem to determine missing sides of right triangles Learn the definitions of the sine, cosine, and tangent ratios of a right triangle Set up proportions using sin, cos, tan to determine missing sides of right triangles. SOLVING RIGHT TRIANGLES. 30  60  90   and   45  45  90   Triangles Calculator for these 2 types of special right triangles. Theorem: The 30-60-90 Triangle:. x w z v t r q. U S jA VlLla urqiJgdh ztksj crKeIsre 4rdv leydJ. Geometry: Common Core (15th Edition) answers to Chapter 8 - Right Triangles and Trigonometry - Mid-Chapter Quiz - Page 515 1 including work step by step written by community members like you. Similarity, Right Triangles, and Trigonometry G-SRT. These three are the main functions that you'll deal with in trigonometry problems. Right Triangle Trigonometry A branch of mathematics dealing with angles, triangles and trigonometric functions such as sine, cosine and tangent. Let the right angle be labelled C and the hypotenuse c. 5 Create your own worksheets like this one with Infinite Precalculus. Know the ratios of the sides of the 30-60-90 special right triangle 4. Trigonometry A ratio of the lengths of the sides of a right triangle is called a trigonometric ratio. It is based on Will Smith’s rap song ‘Gettin’ Jiggy Wit It,’ entitled, ‘Get Triggy Wit It. To use SOH CAH TOA the Triangle must be a Right Triangle. Try this Drag any vertex of the triangle and see how the tangent of A and C are calculated. Choose a test. These two triangles are “special” because, with just a couple pieces of information, we can figure out all their properties. 14 is a B-. Students have been using the unit circle to study trigonometry so far. Practice finding missing side of right triangles. I can identify Pythagorean Triples. prerequisite special right triangles worksheet answers, you are right to find our website which has a comprehensive collection of manuals listed. There is one half-page for 45-45-90 triangles and one half-page for 30-60-90 triangles. A right triangle is a triangle in which one angle is a right angle. Right Triangle Trig Students will apply similarity in right triangles to understand right triangle trigonometry. Similarity, Right Triangles and Trigonometry Common Core Geometry Questions. High school geometry lays the foundation for all higher math, and these thought-provoking worksheets cover everything from the basics through coordinate geometry and trigonometry, in addition to logic problems, so students will be fully prepared for whatever higher math they pursue!. Enrich your knowledge of the characteristics of special right triangles with our quiz. Note Some questions taken from New Visions Classwork Concept Quiz Retake: Special Right Triangles Finished Early? Eightfold (Play With Your Math) Minute to Win It - A Bit Dicey Standards: Common Core HSG. What is the relationship between the legs and hypotenuse of a right triangle and the special right triangles?. ) but is not meant to be shared. Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry, Loose-Leaf Edition Plus MyLab Math with Pearson eText -- 18 Week Access Card Package. In geometry, special right triangles are great to work with because the ratio of their sides will always be the same, making calculations easier. Also, XY2 +YW2 =XW2 Use the Pythagorean Theorem. Students learn to determine angles and side lengths in 30-60-90 and 45-45-90 right triangles using the law of sines and the law of cosines, as well as how to identify similar triangles and determine proportions using proportionality. These two angles form a 30˚-60˚-90˚ right triangle as shown. (G7) Worksheet 7. Answers with radicals must be reduced and rationalized. Using Trig to Find a Missing Angle of a Right Triangle - Explanation, Examples, and Practice Problems  Explanation of Trig Functions with Interactive Visual Guide; Trigonometry Explained by the Unit Circle Quadrants; Inverse Trig Practice Quiz; Trig Ratios Practice Quiz; Reciprocal Trig Functions Explanations and Example Problems. Students will identify and use special right triangles. Some right triangles have special measures and ratios that can also be deduced from the Pythagorean Theorem. Find the exact value of sec 30° - sin 45° + sin 90°. You don't necessarily have to know them off the top of your head, but it could potentially save you a lot of time, so it's worth taking a look at. cos20 = 12 x D. 1 22) 14 B C A 71° 19° 4. IXL will track your score, and the questions will automatically increase in difficulty as you improve!. Question 1 :. m T = ____° What is the measure of angle T to the nearest degree? 17. cos20 = x 12 B. Solve right triangles. Find tan A for the right triangle below: A tree 19 feet tall casts a shadow which forms an angle of 490 with the ground. BH is perpendicular to AC. Tell whether a triangle with the given sides is a right triangle. You may use your Formulas Quiz from Tuesday. RIGHT TRIANGLES Let’s begin our study of trigonometry with measure-ments in the right triangle. Opening - Warm-up: √50 + √32. The tangent function, along with sine and cosine, is one of the three most common trigonometric functions. Students will identify and use special right triangles. Don't wait for more moment, the chance now and set aside your time to pick this. It also contains the unit circle definitions for all trig functions. Right Triangle Trigonometry A branch of mathematics dealing with angles, triangles and trigonometric functions such as sine, cosine and tangent. Using Trig to Find a Missing Side of a Right Triangle - Explanation and Example Problems; Using Trig to Find a Missing Angle of a Right Triangle - Explanation, Examples, and Practice Problems  Explanation of Trig Functions with Interactive Visual Guide; Trigonometry Explained by the Unit Circle Quadrants. 501) Leaning Tower of Pisa (p. Discovery of Special Triangles. We can find the length of the altitude using the Pythagorean Theorem. The three ratios can be found by calculating the ratio of two sides of a right-angled triangle. 30°− 60°− 90° right triangle. Step-by-step explanations are provided for each calculation. Find the length of the missing side. Using the Pythagorean Theorem. Title: Special Right Triangles: 30º - 60º - 90º Author: SFSD Last modified by: SFSD Created Date: 12/19/2007 5:50:00 PM Company: SFSD Other titles. Chapter 8 – Right Triangles and Trigonometry Study Guide/Review 8. To assess student's current understanding of special right triangles students will take their first quick quiz (Version 1) on the clicker. Read about Non-right Triangle Trigonometry (Trigonometry Reference) in our free Electronics Textbook. Using the Pythagorean Theorem. Solving Right Triangles. sight to an object above. See Definition 8 in Some Theorems of Plane Geometry. Chapter 7: Right Triangles and trigonometry. Played 9,825 times. To use SOH CAH TOA the Triangle must be a Right Triangle. See results from the Trig Ratios in Special Right Triangles Quiz on Sporcle, the best trivia site on the internet! Trig Ratios in Special Right Triangles Quiz Stats - By akpgunner play quizzes ad-free. A right triangle is a type of triangle that has one angle that measures 90°. Click here to re-enable them. Triangles are not always right (although they are never wrong), but when they are it opens up an exciting world of possibilities. Special Right Triangles and Right Triangle Trigonometry Reporting Category Triangles Topic Investigating special right triangles and right triangle trigonometry Primary SOL G. Similarity, Right Triangles, and Trigonometry G-SRT. Students learn to determine angles and side lengths in 30-60-90 and 45-45-90 right triangles using the law of sines and the law of cosines, as well as how to identify similar triangles and determine proportions using proportionality. Practice manipulating trigonometric functions, cofunctions, inverses, and applications is the name of the game in this short but extensive problem set. In this section students Construct Special Right Triangles. The first 45 degrees, 45 degrees, and 90 degrees is known as an angle based right triangle. Try this Drag any vertex of the triangle and see how the tangent of A and C are calculated. Any two right triangles with the same two non-right angles are "similar", in the technical sense that their corresponding sides are in proportion. For example, a right triangle may have angles that form simple relationships, such as 45°-45°-90°. Review Geometry topics with mathplane Chain Letters. 3 Special Right Triangles II 7. FREE: PUZZLE MATH: Special Right Triangles. pdf] - Read File Online. A 30-60-90 triangle is a special right triangle with some very special characteristics. Opening - Warm-up: √50 + √32. Pick an existing quiz or create your own for review, formative assessment, and more. Special triangles are a way to get exact values for trigonometric equations. Worksheet. The following is a table of exact values for the trig ratios of the special triangles:. The altitude to the hypotenuse of a right triangle determines another relationship between the segments. Architects use Trigonometry to calculate structural load, roof slopes, ground surfaces and many other aspects, including sun shading and light. Some special measurements of a triangle are 30-60-90 and 45-45-90 triangles. * Find missing side lengths of figures using trigonometric ratios. 501) Leaning Tower of Pisa (p. 3 cm ____ 3. Pythagorean Theorem: a2 + b2 = c2, where a and b are the legs of a right triangle, and c is the hypotenuse. cos70 = x 12 2. Played 9,825 times. Triangles that do not have a right angle are called oblique triangles. Applying Right Triangles. in Egypt in the form of sundial measurements. In the right triangle below, one acute angle is named à (theta), and with respect to that angle, you need to be able to identify the opposite side, the adjacent side, and the hypotenuse of the triangle. How to Find the Length of the Side of a Triangle If You Know the Other Two Sides. special right triangle relationships, not trigonometry ratios. Round your answer to the nearest tenth. Using the Pythagorean theorem and the fact that it has two equal sides, we can find out the ratio of all sides. Cosine Discussion Special Right Triangle Quiz Right Triangles Trig Quiz Right Triangle Trigonometry Test Horizons Project Review Now that you have completed the initial assessments for this module, review the lesson material with the practice activities and extra resources. Special Right Triangles Task Sine vs. Trigonometry Functions and Unit Circle TEST STUDY GUIDE Test covers: Given a right triangle, find 6 trig functions. Discuss two special right triangles, how to derive the formulas to find the lengths of the sides of the triangles by knowing the length of one side, and a few examples using them. Students will identify and use special right triangles. Be careful; in some of these you're just using trig ratios but in others you need to use inverse trig! a. Right: Wrong: Clock << >> Change answer. Leave your answer in simplest radical form. Isosceles Right Triangle: The isosceles right triangle is also called the 45-45-90 triangle because of the measures of the angles. There are some common “special” triangles that you will see over and over again on the new SAT, in school, and even in real life. With some triangles it can be tricky to know the value of the trigonometric function. Powered by Create your own unique website with customizable templates. Y d HASlSlZ BryiVgqh`tFsw jrkeXsDeQrXvHe\dP. It will be collected in class on Friday. Think you've got your head wrapped around Right Triangles and Trigonometry? Put your knowledge to the test. Isosceles Right Triangles 14 30°-60°-90° 15 Mixed practice 16-17 Trigonometry 18 Trigonometry 21 Holiday 22 Trigonometry 23-24 REVIEW Begin Test 25 TEST Tuesday, 1/8 Pythagorean Theorem 1. That is, in the triangle ABC, in which C is the right angle, you should be. STANDARDS The Common Core Standards addressed in this module are: Define trigonometric ratios and solve problems involving right triangles. Then placing these angles on a coordinate plane. Using Trig to Find a Missing Side of a Right Triangle - Explanation and Example Problems; Using Trig to Find a Missing Angle of a Right Triangle - Explanation, Examples, and Practice Problems  Explanation of Trig Functions with Interactive Visual Guide; Trigonometry Explained by the Unit Circle Quadrants. Trigonometry is the study of triangles, which contain angles, of course. Reciprocal Trig Functions. If the altitude is drawn from the vertex of the right angle of a right triangle to its hypotenuse, then the measure of a leg of the triangle is the geometric mean between the. 1 Basic Right Triangle Trigonometry. Worksheet Review Ch. If you need to see more examples, watch the second video. Scroll to a topic and use the resources below to assist your instruction. 8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Monday 9/9. 4 today by practicing the strategies used for solving special right triangles. Played 9,825 times. Angle of Elevation The. Yes, SohCahToa is only for right triangles. Know the ratios of the sides of the 45-45-90 special right triangle 5. Triangle ABC has side lengths 9, 40, and 41. From the triangle we get the ratios as follows: Special Angles: 45 and 90 Next, we consider the 45˚ angle that forms a 45˚-45˚-90˚ right triangle as shown. a) Since x is the angle that we want to find, we will let this angle be our reference angle. SOH CAH TOA tells us which function to use based on which sides were given (the side adjacent to the missing angle, opposite or. * Find missing angle measures of figures using inverse trigonometry ratios. 2 Some Special Triangles TRIGONOMETRY IMPORTANT! It's not enough to know the definitions of the various trigonometric functions. Notes: Special Right Triangles Assignment: Assignment 2 – Special Right Triangles Odd/Selected Answers: Assignment 2 – Special Right Triangles Odd Answers. trigonometry [Gr. Find tan A for the right triangle below: A tree 19 feet tall casts a shadow which forms an angle of 490 with the ground. A 30 60 90 triangle is a special type of right triangle. Guided Lesson - One triangle with three missing parts. Trigonometry 2. Software for math teachers that creates exactly the worksheets you need in a matter of minutes. Chapter 7 investigates side lengths and angles in triangles. This is your chapter test for section 4 on right triangles. SOH CAH TOA is an acronym used to find missing sides and angles of right triangles (its not just a jumble of letters!) Finding Missing Angles: When given 2 sides of a right triangle, we can find a missing angle. 14 2 Spiraled Review: Pythagorean theorem 6. Trigonometry Placement Test The primary content areas assessed by the Trigonometry Placement Test include: Trigonometric functions and identities Right-triangle trigonometry Trigonometric equations and inequalities Graphs of trigonometric functions Special angles (multiples of 30 and 45 degrees). the sides of a right triangle. Carpenters, construction workers and engineers, for example, must possess a thorough understanding of trigonometry. Indian mathematics. If you don't see any interesting for you, use our search form on bottom ↓. Solve for a missing side in 45-45-90 and 30-60-90 special right triangles. Test on right triangles, including the Pythagorean Theorem, similar right triangles, special right triangles, and right triangle trigonometry. 518) Fire Escape (p. Chapter9-(Right(Triangles(and(Trigonometry(©(Ashley(Spencer,(2014((Use$the$Pythagorean$theorem$to$solve$for$the$missingside$length. Triangles Plane Figures Trigonometry Geometry Math Special Right Triangle (I) Activity. Triangles are not always right (although they are never wrong), but when they are it opens up an exciting world of possibilities. Sine, cosine and tangent of an angle represent the ratios that are always true for given angles. High School Geometry- Special Right Triangles Home. Students will then review the Pythagorean Theorem, formulate and test its converse, investigate Pythagorean triples, 45-45-90 and 30-60-90 special right triangles. Develop conceptual understanding:. cos20 = x 12 B. Trigonometry can be used on a daily basis in the workplace. Finding the trigonometric ratios using right triangles. You may only take the exam once. Therefore, if we are given one side we are able to easily find the other sides using the ratio of 1:2:square root of three. Notes: Special Right Triangles Assignment: Assignment 2 – Special Right Triangles Odd/Selected Answers: Assignment 2 – Special Right Triangles Odd Answers. You may use your Formulas Quiz from Tuesday. Similar figures. Use the corner of a piece of notebook paper for a right angle. Test your basic trigonometry(sin, cos, tan) skills free. Solving expressions using 30-60-90 special right triangles. Welcome to Trigonometry Online: Home Algbebra Review To apply and use the law of sin or law of cos formulas to solve triangles for side lengths and angle measures. Right Triangles Test Review Multiple Choice Identify the choice that best completes the statement or answers the question. Find the exact value of tan 0° + cos 90° - sin 0°. A 30 60 90 triangle is a special type of right triangle. $\sin(30) =. Sometimes we have to work backwards to get the angle measurement back so we have to use what a call an inverse trig function. Find h for the given triangle. Students learn to determine angles and side lengths in 30-60-90 and 45-45-90 right triangles using the law of sines and the law of cosines, as well as how to identify similar triangles and determine proportions using proportionality. Discovery of Special Triangles. Trigonometry can be used on a daily basis in the workplace. 485) Skiing (p. Sec 1-3 –Right Triangle Trigonometry Solving with Trigonometry Name: The word trigonometry is of Greek origin and literally translates to “Triangle Measurements”. The theorems cited below will be found there. If you want to read more about that special shape, check our calculator dedicated to the 30° 60° 90° triangle. The Law of. If a house is 40 feet wide and the roof is an isosceles triangle with base angles of 30, how far is it from the bottom edge of the roof to the peak? Round your answer to the nearest tenth. Beecher, Penna, and Bittinger’s Precalculus is known for enabling students to “see the math” through its focus on visualization and early introduction to functions. 8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Read and learn for free about the following article: Special right triangles review Math High school geometry Right triangles & trigonometry Special right triangles. 2 Special Right Triangles; Lesson 7. To find the length of a side you must have the length of one other side and an angle measure other than the right angle. 2 Special Right Triangles 9. This is your chapter test for section 4 on right triangles. 3 Similar Right Triangles Using Geometric Mean : 9. Quiz by akpgunner. 4 Inverse Trig Rations. Special Right Triangles And Right Triangle Trigonometry (1,757 View) Chapter 8 - Right Triangles And Trigonometry - (1,329 View) Chapter 8 - Right Triangles And Trigonometry - Get (4,186 View) Chapter 8 - Right Triangles And Trigonometry - Get (1,217 View) Chapter 4: Congruent Triangles - Augusta County Public (1,106 View). 4 SOLVING RIGHT TRIANGLES 1. Practice Worksheet - I have no idea why I didn't just work off of one triangle, but I didn't. 7 Materials Special Right Triangles activity sheet (attached) Right Triangle Trigonometry activity sheet (attached) Dynamic geometry software package (Assignment can be modified to use paper, compass, and straightedge. Find the value of d. Students have been using the unit circle to study trigonometry so far. Home › By Grade Level › Grade 9 to Grade 12 › Special Right Triangles (Trigonometry Emphasis) Math Quiz A quick quiz to assess ability of this math skill. 518) Skiing (p 501). Special Right Triangles. Complete the proportion. This is not the case with some very special triangles. Angle of Elevation and Depression. Chapter Review. * Find missing side lengths of figures using trigonometric ratios. 1 feet above the ground. 4/18 – Right Triangle Trigonometry Notes: Right Triangle Trigonometry Assignment: Assignment 3 – Right Triangle Trig Odd/Selected Answers: Assignment 3 – Right Triangle Trig Odd. Sometimes we have to work backwards to get the angle measurement back so we have to use what a call an inverse trig function. 518) Fire Escape (p. Trig functions take an angle and return a percentage. The word Trigonometry can be broken into the parts Tri, gon, and metry, which. Scroll down the page if you need more examples and explanations on how to derive and use the trig ratios of special angles. Get Started. Right Triangles and Trigonometry. A diagram is shown below. I can identify Pythagorean Triples. Triangle Trig. This Right Triangle Trigonometry Presentation is suitable for 10th - 12th Grade. In this exercise you will write an algebraic proof with the following Given and Prove statements. Right triangles have played a part in the story of humankind extending back to the earliest of our civilizations. Use special right triangles to find the value of u Unit 5 Practice Test: Right Triangle Trigonometry DRAFT. The first 45 degrees, 45 degrees, and 90 degrees is known as an angle based right triangle. 5 Law of Sines and Cosines 8. 2 Lesson WWhat You Will Learnhat You Will Learn Find side lengths in special right triangles. Determine the lengths of sides of 30°-60°-90° triangles. Learn vocabulary, terms, and more with flashcards, games, and other study tools. For practice on this and more, take this quiz. Please do not copy or share the Answer Keys or other subscriber content. The three page worksheet contains twelve questions. To find the measure of an angle you must have the measures of two sides of the triangle. There is also a perpendicular from one vertex. Available for Pre-Algebra, Algebra 1, Geometry, Algebra 2, Precalculus, and Calculus. to the nearest tenth, if. 6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. Use trigonometry to solve for the missing value. S t hAPlJlR sryi_gYhntssG trIe[sKebrGvWeNdg. Use properties of 30-60-90 special right triangles. Reciprocal trig functions. Lesson 1: Quiz - Right Triangle Trig! Lesson 12:. Example The legs ofa 45°-45°-90°triangle, a andb, are equal in measure. Unit 6 Right Triangle Relationships and Trigonometry Test planned for Jan. Unit 5 Test Review (Pythagorean Theorem, Special Right Triangles, Trig) by Courtney Wilkins on Jan 15, 2013. Homework/Answers. Please answer the questions on your own without the use of notes. Find the requested unknown side of the following triangles. use special triangle patterns (30-60-90 and 45-45-90) to determine a missing measure; find the area or perimeter of a simple polygon with right triangles using a variety of methods including trig, Pythagorean Theorem, special triangles, etc. This will test your knowledge of right triangles and complicated concepts with right triangles. Determine the lengths of sides of 30°-60°-90° triangles. Cosine, Sine, and Tangent are used in Geometry with special right triangles, to find missing angles and sides. Key Words. The legs of an isosceles right triangle measure 10 inches. Mathematics Capstone Course Developed by Dr. Inverse trig. ratios Solving right triangles Multi-step special. To use SOH CAH TOA the Triangle must be a Right Triangle. 2 Finding Values of Trig Functions with the Unit Circle Notes 8/22/19 Day 4 HW: Special Right Triangle & Rationalizing the Denominator Extra Practice WS Unit Circle Notes. 1) tan A 40 30 50 AB C 2) sin Z 40 30 50 Z YX 3) cos C 2821 C35 B A 4) sin A 8 1517 BA C 5) tan Z 9 40. Students have been using the unit circle to study trigonometry so far. The goal is to make this a richer unit than it was last year. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. When numbers are rounded, it means that your answer isn't exact, and that's something that mathematicians do not like. Michael Bolling, Virginia Department of Education!! Right&Triangle&Sports& I. Sines and cosines are two trig functions that factor heavily into any study of trigonometry; they have their own. Use trigonometry to solve for the missing value. Recall each reference triangle and accurately construct it. Good luck — the Stickman is counting on you. The perimeter of an equilateral triangle is 39 cm. Solve problems using the Pythagorean theorem. The values of trig functions of these specific angles can be represented by known ratios, and are good to commit to memory to help you work through problems faster. Chapter9–(Right(Triangles(and(Trigonometry(©(Ashley(Spencer,(2014((Use$the$Pythagorean$theorem$to$solve$for$the$missingside$length. Geometry: Common Core (15th Edition) answers to Chapter 8 - Right Triangles and Trigonometry - Mid-Chapter Quiz - Page 515 1 including work step by step written by community members like you. Basic Trigonometric. 501) Leaning Tower of Pisa (p. 1) 10 45° x 45° 5 2) 7 45° x 45° 14 3) 9 45° x 45° 18 4) 45° 9 x 45° 9 2 5) 45° 5 2 x 45° 5 2 2 6) 9 6 45° x 45° 9 6 2 7) 60° 9 x 60° 9 3 4 8) 5 60° x 60° 5 3 3-1-. You don't necessarily have to know them off the top of your head, but it could potentially save you a lot of time, so it's worth taking a look at. 7 8 2/1 2/4 Chapter 7 Review To review right triangles and trigonometry. There is one half-page for 45-45-90 triangles and one half-page for 30-60-90 triangles. 3 Trig Applications No Notes - Only Homework 6. The two special triangles you need to know are the isosceles (or 45-45-90) and 30-60-90 right triangles.