Name: ________________________ Class: ___________________ Date: __________ ID: A

1

1

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

1. Use the Law of Sines to find x. Let a = 85, A 34.6.

a. 132b. 134c. 133d. 135

2. Use the Law of Sines to find x. Let c =21, A 58.

a. 24b. 25c. 46d. 23

3. Use the Law of Sines to find angle C. Let a = 28, and c = 13.

a. 24b. 25c. 23d. 30

4. Solve the triangle using the Law of Sines. Let A 54, B 16.

a. C 120, b 19, a 57b. C 112, b 17, a 56c. C 109, b 20, a 59d. C 110, b 19, a 56

Name: ________________________ ID: A

2

5. A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, c = 6 mi apart, to be m 28, k 51.

(a) Find the distance of the plane from point A.(b) Find the elevation of the plane.

a. The distance of the plane from point A = 4.8, the elevation of the plane = 4.4b. The distance of the plane from point A = 4.8, the elevation of the plane = 2.2c. The distance of the plane from point A = 2.2, the elevation of the plane = 2.4d. The distance of the plane from point A = 5.9, the elevation of the plane = 2.2

6. To find the distance across a river, a surveyor chooses points A and B, which are 197 ft apart on one side of the river (see the figure). She then chooses a reference point (C) on the opposite side of the river and finds that A 47 and B 70. Approximate the distance from A to C.

a. 209 ftb. 206 ftc. 207 ftd. 208 ft

Name: ________________________ ID: A

3

7. A tree on a hillside casts a shadow b = 209 ft down the hill. If the angle of inclination of the hillside is 22 to the

horizontal and the angle of elevation of the sun is 54, find the height of the tree.

a. The height of the tree is 188 ftb. The height of the tree is 190 ftc. The height of the tree is 184 ftd. The height of the tree is 186 ft

Numeric Response

8. Use the Law of Sines to find the indicated angle . Please round the answer to the nearest tenth.

= __________

9. Use the Law of Sines to find the indicated side x. Please round the answer to the nearest tenth.

x __________

10. Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point C on land such that CAB 48.8. He also measures CA as 318 ft and CB as 523 ft. Find the distance between A and B. Please round the answer to the nearest tenth.

__________ ft

Name: ________________________ ID: A

4

11. A short-wave radio antenna is supported by two guy wires, 155 ft and 175 ft long. Each wire is attached to the top of the antenna and anchored to the ground, at two anchor points on opposite sides of the antenna. The shorter wire makes an angle of 63 with the ground. How far apart are the anchor points? Please round the answer to the nearest tenth.

__________ ft

12. A water tower 40 m tall is located at the top of a hill. From a distance of 120 m down the hill, it is observed that the angle formed between the top and base of the tower is 5. Find the angle of inclination of the hill. Please round the answer to the nearest tenth.

__________

13. For the triangle shown, find the length AD. Please round the answer to the nearest hundredth.

AD = __________

Name: ________________________ ID: A

5

Short Answer

14. Solve the triangle using the Law of Sines. Please round the answer to the nearest tenth.

B __________

C __________

c = __________

15.

(a) For the triangle shown, find BCD. Please round the answer to the nearest tenth.

BCD = __________

(b) For the triangle shown, find DCA. Please round the answer to the nearest tenth.

DCA = __________