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Name: Geometry Step-by-Step Chapter 9 Show all steps and then explain each step you used in solving the problem. Find x. Steps Explanation 2. Write a similarity statement about the three triangles shown in the diagram. 3. Find SQ. Steps Explanation Find the unknown side length. Simplify answers that are radicals. Tell whether the side lengths form a Pythagorean triple. Find the unknown side length. Simplify answers that are radicals. Tell whether the side lengths form a Pythagorean triple. 7. 15, 20, 25 Steps Explanation 8. Decide whether the numbers can represent the side lengths of a triangle. If they can, classify the triangle as right, acute, or obtuse. 2, 6, 6 9. 1,2,8 Steps Explanation 10. Decide whether the numbers can represent the side lengths of a triangle. If they can, classify the triangle as right, acute, or obtuse. 27, 36, 45 11. Decide whether the numbers can represent the side lengths of a triangle. If they can, classify the triangle as right, acute, or obtuse. 2.5, 1.5, 4 12. Decide whether the numbers can represent the side lengths of a triangle. If they can, classify the triangle as right, acute, or obtuse. 12, 16, 25 13. Steps Explanation Find the value of each variable. Write answers in simplest radical form. Find the value of each variable. Write answers in simplest radical form. Steps Explanation Find the sine, the cosine, and the tangent of the acute angle A of the triangle. Express each value as a decimal rounded to four places. 17. Find the sine, the cosine, and the tangent of the acute angle A of the triangle. Express each value as a decimal rounded to four places. 18. 19. Steps Explanation Use trigonometric ratios to find the value of each variable. Round decimals to the nearest tenth. 21. In a college soccer league, the smallest field allowed is a rectangle 65 yards wide and 110 yards long. The largest field allowed is a rectangle 80 yards wide and 120 yards long. To the nearest yard, how much longer is the diagonal of the largest field than the diagonal of the smallest field? 22. Find the unknown side length. Simplify answers that are radicals. Tell whether the side lengths form a Pythagorean triple. 23. Steps Explanation 24. Find the value of each variable. Write answers in simplest radical form. ANSWERS to Geometry Step-by-Step Chapter 9: 1. 12 2. 3. 2 sqrt3 4. 2; no 5. 14; no 6. 16.5; no 7. yes; right 8. yes; acute 9. no 10. yes; right 11. no 12. yes; obtuse 13. 14. 15. 16. sin A = 0.6; cos A = 0.8; tan A = 0.75 17. sin A = 0.6; cos A = 0.8; tan A = 0.75 18. sin A = 0.4854; cos A = 0.8738; tan A = 0.5556 19. 7.2 20. 8.8 21. 16 yd. 22. 7.6; no 23. 24.