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Learning Objective We will determine1 how to find the side lengths of right triangles by using the Tangent Ratio2. What are we going to do? What is Ratio means?_______. CFU Activate Prior Knowledge The Greek letter theta ( ) is used to represent the measure of an angle in a right triangle. Opposite(Opp) – Is a position on the other side of a specific angle from; facing. Hypotenuse Opposite Adjacent(Adj) -next to something else. Hypotenuse(Hyp )- the longest side of a right triangle, opposite the right angle (90 ). o Adjacent Students, you already know identify the sides in a right triangle. Today, we will learn how to find the side lengths of a right triangles by using the Tangent Ratio. Make Connection On your white board, write the opposite side of: Angle A Angle B CFU B C A On your white board, write the Adjacent side of: Angle A Angle B CFU B C A 1 Figure out 2 A ratio is a comparison between two different things, written as a fraction. Vocabulary

Concept Development Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles. The main functions in trigonometry are Sine, Cosine and Tangent (often abbreviated1 to sin, cos and tan.) On your whiteboard, Identify the following: What is the ratio for Tan(T)? What is the ratio for Tan(G)? In your own words, describe the Trigonometry. In mathematic, Trigonometry is_____. CFU Tangent of an angle is the length of the opposite side (O) divided by the length of the adjacent side (A). Tan(T) = 8/15 G T R 17 8 15 Tan(G) = 15/8 *You can use a calculator to approximate the sine, cosine, and the tangent. Make sure that your calculator is in degree mode. The table shows values of each function. 1 shortened; Vocabulary

1. Write the equation that expresses the measure Skill Development/Guided Practice Tangent of an angle is the length of the opposite side (O) divided by the length of the adjacent side (A). Steps to find Tangent Ratio 1 2 3 4 How did I/you know which angle to use? How did I/you identify the Opposite and Adjacent sides? How did I/you find the unknown side length? CFU 1 2 3 Identify the angle to “look” through. Identify the Opp and Adj side to the angle. Write down the Tangent Ratio. Solve for the Unknown. 1. Write the equation that expresses the measure of side BC. Then solve the equation, expressing your answer to the nearest tenth. 2. Use the tangent to find the length of side AC. Express your answer to the nearest tenth. Remember the Concept

Check for Understanding Skill Development/Guided Practice Tangent of an angle is the length of the opposite side (O) divided by the length of the adjacent side (A). Steps to find Tangent Ratio 1 2 3 4 How did I/you know which angle to use? How did I/you identify the Opposite and Adjacent sides? How did I/you find the unknown side length? CFU 1 2 3 Identify the angle to “look” through. Identify the Opp and Adj side to the angle. Write down the Tangent Ratio. Solve for the Unknown. 1. Find the measure of ∠A. Use the inverse tangent (tan ) function of your calculator. Express your answer to the nearest degree. Arctangent - a mathematical function that is the inverse of the tangent function. 2. Find the measure of ∠R. Use the inverse tangent (tan−1) function of your calculator. Express your answer to the nearest degree. −1 Check for Understanding A Explain to B: How did I find the angle A?

The tree is about 76 feet tall. Write the ratio Substitute values Relevance Reason #1: Tangent Ratio are used in finding the height. You are measuring the height of a Sitka spruce tree in Alaska. You stand 45 feet from the base of the tree. You measure the angle of elevation from a point on the ground to the top of the top of the tree to be 59°. To estimate the height of the tree, you can write a trigonometric ratio that involves the height h and the known length of 45 feet. tan 59° = opposite adjacent Write the ratio tan 59° = h 45 Check for Understanding Does anyone else have another reason why it is relevant to use verb tense correctly? Which reason is most relevant to you? Why? The tree is about 76 feet tall. Substitute values 45 tan 59° = h Multiply each side by 45 45 (1.6643) ≈ h Sample Item 75.9 ≈ h Simplify Find tan T. Leave answer as a fraction. = Relevance Reason #2: Know how to find geometric mean will help you do well on tests: (PSAT, SAT, ACT, GRE, GMAT, LSAT, etc..). 34

What did you learn today about how to find the side lengths of right triangles by using the Tangent Ratio. Word Bank Tangent Opposite Adjacent Arc-tangent TOA SUMMARY CLOSURE Today, I learned how to __________________ ______________________________________________________________.