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Geometry B Unit 6 Practice Test ANSWERS Name Date Block Directions: This test is written to cover Unit 6. Please answer each question to the best of your ability. If multiple steps are required, it is expected that you will show those steps. If the appropriate work is not shown, then points may be deducted. 1. Fill in the following trigonometric ratio, using the triangle at the right. Leave your answers as fractions. (3 pts) a. sin R 3 5 b. cosT 3 5 c. tan T 4 3 2. Use your calculator to find the following. Round to four decimal places, if necessary. (3 pts) a. sin 42 0.6691 b. cos89 c. tan55 0.0175 1.4281 3. Use a calculator to find each angle measure to the nearest tenth of a degree. (3 pts) a. sin 1 (0.28) 16.3° 5 b. cos1 65.4° 12 c. tan 1 (3.43) 73.7° 4. To the nearest tenth of an inch, what is the length of EF, the longest side of the sail shown to the right? (2 pts) 28 EF 28 EF sin 65 sin 65 EF 30.9 inches 5. Solve the triangles. Show work for credit. Round side lengths the same as the given side and round all angles to the nearest tenth. (12 pts) a. XW = 18.3 312 XW 2 362 XW 2 362 312 335 XW 18.3 mY = 30.6° mX = 59.4° 31 36 31 X sin 1 36 31 36 31 Y cos1 36 X 59.4 X 30.6 sin X cosY b. mS = 24° ST = 50.5 SU = 55.3 mT 66 90 180 mT 24 ST 22.5 ST 22.5 tan 66 tan 66 ST 50.5 22.5 SU 22.5 SU cos66 SU 55.3 cos66 6. A road sign says that the road ahead has a 7% grade. To the nearest hundredth of a degree, find the angle the road makes with the horizontal. (2 pts) 7 100 1 A tan 0.07 tan A A 4.00 7. Ben is on the diving board at the pool. Jenna is in the pool, and a lifeguard sits at her station on the opposite end of the pool. Classify each angle as an angle of elevation or angle of depression. (2 pts) 1 depression 2 elevation 3 depression 4 elevation 8. A ranger in a lookout spots a fire in the distance. The angle of depression to the fire is 4°, and the lookout tower is 32 meters tall. What is the horizontal distance to the fire? Round to the nearest meter. (3 pts) 32 tan 4 x 32 x tan 4 x 458 meters 4° 32 4° x 9. When the angle of elevation to the sun is 82°, a monument casts a shadow that is 5.1 feet long. What is the height of the monument? Round to the nearest tenth of a foot. (3 pts) h 5.1 h 5.1 tan 82 tan 82 h h 36.3 feet 82° 5.1 10.Use the Law of Sines or Law of Cosines to find the missing side or angle. Show work for credit. Round all answers to the nearest tenth. (8 pts) a. Find mR . 85.4° b. Find HG. 61.1 sin 43 sin R 16.9 24.7 16.9sin R 24.7sin 43 sin 35 sin116 39 HG HG sin 35 39sin116 24.7sin 43 .9967... 16.9 R sin 1 (.9967...) 85.4 HG sin R c. Find FE. 10.0 FE 2 5.82 6.32 2(5.8)(6.3)cos112 FE 2 100.706... FE 10.0 39sin116 sin 35 HG 61.1 d. Find mS . 39.7° 6.22 8.82 9.42 2(8.8)(9.4)cos S 127.36 165.44cos S 127.36 cos S 165.44 127.36 S cos1 39.7 165.44 11.Find the exact (radical) values of x and y for the following.* x =8 2 7 2 2 7 2 y= 2 x= y=8 a. b. x =6 x =12 y= 2 3 y= 6 3 c. d. 12.Find the following values.* sin30 = (8 pts) 1 2 (3 pts) tan30 = sin 45 = 2 2 tan 45 = 1 sin 60 = 3 2 tan 60 = cos30 = 3 2 cos 60 = cos 45 = 2 2 3 3 3 1 2 *these two problems will be done with no calculator, and will be done first…you will then hand in these problems in exchange for the rest of the test