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Learning Objective We will determine1 how to use trigonometry ratios to solve problems involving right triangles. What are we going to do? What is determine means?_______. CFU Activate Prior Knowledge The Miwok Indian Tribe that at one time lived in the area which we now know as Delhi used the word. Hypotenuse Opposite to help them remember the trigonometric ratios. Adjacent Find the height of the tree using Trig Ratios: Students, you already know how to identify and use SOH-CAH TOA. Today, we will learn how to use trig. ratios to solve problems involving right triangles. Make Connection 69 Ft y               1 Figure out Vocabulary    

Skill Development/Guided Practice Trigonometric ratios are formed by comparing the lengths of two sides of a right triangle from the “viewpoint” of a given acute angle. Steps to find Trig Ratio 1 2 3 4 How did I/you know which angle to use? How did I/you identify the Opposite, Adjacent, & Hypotenuse sides? How did I/you find the unknown side length? CFU 1 2 3 Identify the angle to “look” through. Identify the Opp , Adj , and Hyp side to the angle. Write down the Ratio. SOH-CAH-TOA Solve for the Unknown. 1. A painter is placing a ladder to reach the third story window, which is 30 feet above the ground and makes an angle with the ground of 80°. 2. Suppose a new regulation states that the maximum angle of a ramp for wheelchairs is 7°. At least how long must the new ramp be? Round to the nearest tenth of a foot. Remember the Concept *switch tan with x 30 ft.   80° x ft. The base of the ladder needs to be positioned 5.3 ft. out from the building.

Skill Development/Guided Practice Trigonometric ratios are formed by comparing the lengths of two sides of a right triangle from the “viewpoint” of a given acute angle. Steps to find Trig Ratio 1 2 3 4 How did I/you know which angle to use? How did I/you identify the Opposite, Adjacent, & Hypotenuse sides? How did I/you find the unknown side length? CFU 1 2 3 Identify the angle to “look” through. Identify the Opp , Adj , and Hyp side to the angle. Write down the Ratio. SOH-CAH-TOA Solve for the Unknown. 1. A drawbridge at the entrance to an ancient castle is raised and lowered by a pair of chains. Find the height of the suspension point of the chain, to the nearest tenth of a meter. 2. A building casts a 37 m shadow when the Sun is at an angle of 28° to the vertical. How tall is the building, to the nearest meter? Use a trigonometric ratio to find the distance FE. Pythagorean Theorem Angle A 50 Angle C 40 4.3

The tree is about 76 feet tall. Write the ratio Substitute values Relevance Reason #1: Trig 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 The tree is about 76 feet tall. 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? Substitute values 45 tan 59° = h Multiply each side by 45 45 (1.6643) ≈ h Sample Item 75.9 ≈ h Simplify Find Sin, Cos, Tan of T. Leave answer as a fraction.   Relevance Reason #2: Know how to find Trig Ratios will help you do well on tests: (PSAT, SAT, ACT, GRE, GMAT, LSAT, etc..).    

What did you learn today about how to use the trigonometry ratios to solve problems involving right triangles. Word Bank Unit Circle 45-45-90 Triangle 30-60-90 Triangle . SUMMARY CLOSURE Today, I learned how to __________________ ______________________________________________________________.