Let be an acute angle. Use a calculator to approximate the measure of to the nearest tenth of a degree.

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1 Ch. 9 Test - Geo H. Let be an acute angle. Use a calculator to approximate the measure of to the nearest tenth of a degree a. about 58.0 c. about 1.0 b. about 49.4 d. about 32.0 a. about 52.2 c. about b. about 40.7 d. about 37.8 a. about 27.5 c. about 0.06 b. about 22.8 d. about Find the value of x x a. x = 119 c. x = 365 b. x = 17 d. x = Find the value of x. 17 x 14 a. x = 93 c. x = 93 b. x = 3 d. x = A castle guard is standing on the opposite side of an 8-foot moat and wants to reach a window that is 15 feet above the ground. The guard props a ladder against the castle wall to form a right triangle as shown. Approximate the length of the ladder needed to reach the window to the nearest tenth of a foot.

2 15 ft 8 ft Not drawn to scale a ft c ft b ft d. about 12.7 ft 7. An adventure company wants to run a zip line from the top of one building that is 130 feet tall to the top of another building that is 30 feet tall. The two buildings are 72 feet apart. Estimate the length (in feet) of the zip line. Round your answer to the nearest tenth. a. about 69.4 ft c. about ft b. about ft d. about ft 8. In the diagram, BC = Find AB. Write your answer in simplest form. a. 24 c b. 12 d In the diagram, 2 and 2. Find AB. Write your answer in simplest form.

3 a c b. 24 d. 48 Find the value(s) of the variable(s). If necessary, round decimal answers to the nearest tenth x a c. 3.8 b d x 7 y 33 a., c., b., d., 12. A car is traveling along a road that makes a 10 angle with the ground. Find the elevation of the car on a stretch of road that extends horizontally 86 meters. Round your answer to the nearest tenth.

4 10 86 m Not drawn to scale a. about 15.2 m c. about 55.8 m b. about m d. about m 13. In an obstacle course, participants climb to the top of a tower and use a zip line to travel across a mud pit. The zip line extends from the top of a tower to a point on the ground 48.2 feet away from the base of the tower. The angle of elevation of the zip line is 33. Estimate the length of the zip line to the nearest tenth of a foot ft Not drawn to scale 33 a. about 74.2 ft c. about 88.5 ft b. about 31.3 ft d. about 57.5 ft 14. A parasailer is attached to a boat with a rope. While parasailing, the angle of depression to the boat is 25. When the parasailer is attached to the boat with a 300-foot rope, how high above the boat is he? Round your answer to the nearest tenth of a foot. a. about ft c. about ft b. about 82.8 ft d. about ft Solve the triangle. Round decimal answers to the nearest tenth.

5 15. H F G a.,, c.,, b.,, d.,, 16. H y F 10 G 73 c a.,, c.,, b.,, d.,, 17. A carpenter is constructing a staircase in a house. The distance from the first floor to the basement is 10.3 feet. The staircase will be 17.9 feet long. What angle do the stairs make with the basement floor? a. about 60.1 c. about 35.1 b. about 29.9 d. about Find the area of the triangle. Round your answer to the nearest tenth. A C B a. about units 2 c. about units 2 b. about units 2 d. about units 2

6 19. Two mountain climbers are standing 3600 feet apart on opposite sides of a mountain. The mountain s angle of elevation on the east side is 30, while the west side has a much steeper incline of 50. How far does the climber on the west side need to climb to reach the top of the mountain? a. about ft c. about ft b. about ft d. about ft 20. Use a special right triangle to find the tangent of a 60 angle. a. b. 2 c. d.

7 Ch. 9 Test - Geo H. Answer Section 1. ANS: A PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.6 KEY: inverse trigonometric ratios 2. ANS: A PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.6 KEY: inverse trigonometric ratios 3. ANS: D PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.6 KEY: inverse trigonometric ratios 4. ANS: D PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.1 KEY: Pythagorean Theorem NOT: Example 1 5. ANS: C PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.1 KEY: Pythagorean Theorem 6. ANS: A PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.1 KEY: Pythagorean Theorem application NOT: Example ANS: B PTS: 1 DIF: Level 2 REF: Geometry Sec. 9.1 KEY: Pythagorean Theorem application NOT: Example ANS: A PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.2 KEY: special right triangles NOT: Example 1 9. ANS: D PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.2 KEY: special right triangles NOT: Example ANS: C PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.4 NAT: HSG-SRT.C.6 HSG-SRT.C.8 KEY: tangent 11. ANS: C PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.5 NAT: HSG-SRT.C.6 HSG-SRT.C.7 HSG-SRT.C.8 KEY: sine cosine NOT: Example ANS: A PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.4 NAT: HSG-SRT.C.6 HSG-SRT.C.8 KEY: angle of elevation application NOT: Example ANS: D PTS: 1 DIF: Level 2 REF: Geometry Sec. 9.4 NAT: HSG-SRT.C.6 HSG-SRT.C.8 KEY: angle of elevation application NOT: Example ANS: D PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.5 NAT: HSG-SRT.C.6 HSG-SRT.C.7 HSG-SRT.C.8 KEY: sine cosine application NOT: Example ANS: A PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.6 KEY: solve a right triangle NOT: Example ANS: D PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.6 KEY: solve a right triangle

8 NOT: Example ANS: C PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.6 HSG-MG.A.1 HSG-MG.A.3 KEY: application inverse trigonometric ratios NOT: Example ANS: B PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.7 NAT: HSG-SRT.D.9 KEY: area of a triangle 19. ANS: C PTS: 1 DIF: Level 2 REF: Geometry Sec. 9.7 NAT: HSG-SRT.D.10 HSG-SRT.D.11 HSG-MG.A.3 KEY: Law of Sines application NOT: Example ANS: A PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.4 NAT: HSG-SRT.C.6 HSG-SRT.C.8 KEY: tangent NOT: Example 3