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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.

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Essential Questions

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

  2. 5.2 Apply the Tangent Ratio B c a CAH TOA A C b Trigonometric Ratios SOHCAHTOA SOH

  3. 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

  4. 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. 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.

  6. 5.2 Apply the Tangent Ratio Checkpoint. Complete the following exercises. • Find tan A and tan B. Round your answer to four decimal places.

  7. 5.2 Apply the Tangent Ratio Checkpoint. Complete the following exercises. • Find the value of x. Round to the nearest tenth.

  8. 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 ________.

  9. 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.

  10. 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.

  11. 5.2 Apply the Tangent Ratio Pg. 173, 5.2 #1-25

  12. 5.3 Apply the Sine and Cosine Ratios Pg. 218, 6.4 #1-32

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