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

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

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

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

Apply the Tangent Ratio 5.2 Apply the Tangent Ratio Example 2 Find a leg length 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.

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

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

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

Apply the Tangent Ratio 5.2 Apply the Tangent Ratio Example 4 Estimate height using tangent 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. The flagpole is about _____ feet tall. 19

Apply the Tangent Ratio 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.

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

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