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Name _______________________________________ Date __________________ Class __________________ LESSON 8-3 Practice A Solving Right Triangles In Exercises 1–3, fill in the blanks to complete the description of the inverse trigonometric ratios. 1. If sin A x, then sin1 x ________. 2. If cos A ________, then cos1 x mA. 3. If tan A x, then ________ mA. Use the given trigonometric ratio to determine whether 1 or 2 is A in each exercise. 4. sin A 4 ________ 5 5. cos A 4 ________ 5 6. tan A 3 ________ 4 7. sin A 3 ________ 5 8. cos A 3 ________ 5 9. tan A 4 ________ 3 Use a calculator to find each angle measure to the nearest degree. 10. sin1 (0.33) ________ 11. cos1 (0.47) ________ 12. tan1 (1.21) ________ 9 13. sin1 ________ 10 1 14. cos1 5 3 15. tan1 2 ________ 4 ________ Use a calculator and inverse trigonometric ratios to find the unknown side lengths and angle measures. Round lengths to the nearest hundredth and angle measures to the nearest degree. 16. 17. AC ________ mB ________ mC ________ 18. DE ________ EF ________ mD ________ GH ________ mH ________ mI ________ XYZ has vertices X(6, 6), Y(6, 3), and Z(1, 3). Complete Exercises 19–21 to find the side lengths to the nearest hundredth and the angle measures to the nearest degree. 19. Plot the points and draw XYZ. 20. Tell which angle is the right angle. ________ 21. Find XY and YZ from the graph. Use the Pythagorean Theorem to find XZ. XY ________ YZ ________ XZ ________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 8-19 Holt Geometry Name _______________________________________ Date __________________ Class __________________ LESSON 8-3 Practice B Solving Right Triangles Use the given trigonometric ratio to determine which angle of the triangle is A. 1. sin A 8 ________ 17 2. cos A 15 ________ 17 3. tan A 15 ________ 8 4. sin A 15 ________ 17 5. cos A 8 ________ 17 6. tan A 8 ________ 15 Use a calculator to find each angle measure to the nearest degree. 7. sin1 (0.82) ________ 3 10. sin1 8 ________ 11 8. cos1 ________ 12 11. cos1 (0.23) ________ 9. tan1 (5.03) ________ 1 12. tan1 9 ________ Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree. 13. 14. 15. ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ 16. 17. 18. ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ For each triangle, find all three side lengths to the nearest hundredth and all three angle measures to the nearest degree. 19. B(2, 4), C(3, 3), D(2, 3) ________________________________________________________________________________________ 20. L(1, 6), M(1, 6), N(1, 1) ________________________________________________________________________________________ 21. X(4, 5), Y(3, 5), Z(3, 4) ________________________________________________________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 8-20 Holt Geometry Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. A11 Holt Geometry