Essential Questions

Wednesday, February 3 Essential Questions • How do I use the sine, cosine, and tangent ratios to solve triangles?

5.2 Apply the Tangent Ratio B c a CAH TOA A C b Trigonometric Ratios SOHCAHTOA SOH

5.2 Apply the Tangent Ratio Let rABC be a right triangle with acute The tangent of (written as tan A) is defined as follows: Tangent Ratio

5.2 Apply the Tangent Ratio In the right triangle, rXYZ, and are _______________ angles. You can see that the tangent ratios of the _________________ angles are ___________. Find tangent ratios Example 1 Find tan X and tan Y. Write each answer as a fraction and as a decimal rounded to four places. complementary complementary reciprocals

5.2 Apply the Tangent Ratio Find a leg length Example 2 Find the value of x. Use the tangent of an acute angle to find a leg length. Write a ratio for tangent of 25o. Substitute. Multiply each side by ____. Use a calculator to find tan 25o. Simplify.

5.2 Apply the Tangent Ratio Checkpoint. Complete the following exercises. • Find tan A and tan B. Round your answer to four decimal places.

5.2 Apply the Tangent Ratio Checkpoint. Complete the following exercises. • Find the value of x. Round to the nearest tenth.

5.2 Apply the Tangent Ratio Compare the tangent ratios for similar triangles Example 3 Find tan X and tan Y for similar triangles. Then compare the tangent ratios. equivalent The values of tan X and tan Y for the similar triangles are ________.

5.2 Apply the Tangent Ratio Estimate height using tangent Example 4 Find the height h of the flagpole to the nearest foot. Write ratio for tangent of 70o. Substitute. Multiply each side by ___. Use a calculator to simplify. 19 The flagpole is about _____ feet tall.

5.2 Apply the Tangent Ratio Checkpoint. Complete the following exercises. • Find the height h of the flagpole in Example 4 to the nearest foot if the angle is 75o.

5.2 Apply the Tangent Ratio Pg. 173, 5.2 #1-25

5.3 Apply the Sine and Cosine Ratios Pg. 218, 6.4 #1-32

Essential Questions