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Name ________________________________________ Date __________________ Class __________________ LESSON 13-1 Tangent Ratio Practice and Problem Solving: A/B Identify the relationships in the figure to the right. 1. tanX = 3. tan−1 WX = VW = m∠_____ WX 5. tanX × tanV = _____ 2. tanV = 4. tan−1 WX = m∠_____ VW 6. tan−1 VW + tan−1 WX = _____° WX VW Use a calculator to find each tangent or inverse tangent. Round tangents to the nearest 0.01 and angles to the nearest 0.1 degree. Check the inverse tangents by finding the tangent of each angle. 7. tan23° ≈ _____________ 10. tan−10.14 ≈ _____________° tan _____________° ≈ 0.14 8. tan43° ≈ _____________ 11. tan−11= _____________° 9. tan47° ≈ _____________ 12. tan−16.1 ≈ _____________° tan _____________° = 1 tan _____________° ≈ 6.1 Solve Problems 13–16 using tangent ratios and a calculator. Refer to the figure to the right of each problem. 13. To the nearest hundredth, what is tanM in +LMN ? ________ 14. Write a ratio that gives tanS. ________ Find the value of tanS to the nearest hundredth. ________ Use the inverse tangent function on your calculator to find the angle with that tangent. ________ 15. Write and solve a tangent equation to find the distance from C to E to the nearest 0.1 meter. ________ meters 16. The glide slope is the path a plane uses while it is landing on a runway. The glide slope usually makes a 3° angle with the ground. A plane is on the glide slope and is 1 mile (5280 feet) from touchdown. Find EF, the plane’s altitude, to the nearest foot. Show your work. _________________________________________________________________________________________ _________________________________________________________________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 253 Name ________________________________________ Date __________________ Class __________________ LESSON 13-2 Sine and Cosine Ratios Practice and Problem Solving: A/B After verifying that the triangle to the right is a right triangle, use a calculator to find the given measures. Give ratios to the nearest hundredth and angles to the nearest degree. 1. Use the Pythagorean Theorem to confirm that the triangle is a right triangle. Show your work. ________________________________________________________________ 2. sin∠1 = ≈ _________________ 3. sin∠2 = 4. cos∠1 = = _________________ 5. cos∠2 = = _______________________ ≈ _______________________ 6. Show how to find m∠1 using the inverse sine of ∠1. _________________________________________________________________________________________ 7. Show how to find m∠2 using the inverse sine of ∠2. _________________________________________________________________________________________ Use a calculator and trigonometric ratios to find each length. Round to the nearest hundredth. 8. 9. BD = _________________ 10. QP = _________________ ST = _________________ Use sine and cosine ratios to solve Problems 11–13. 11. Find the perimeter of the triangle. Round to the nearest 0.1 centimeter. _________________ 12. To the nearest 0.1 inch, what is the length of the hypotenuse of the springboard shown to the right? _________________ 13. What is the height of the springboard (the dotted line)? _________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 258