North Carolina Math 2 Transition Edition Unit 5 Assessment: Trigonometry

Transcription

1 Name: Class: _ Date: _ North Carolina Math 2 Transition Edition Unit 5 Assessment: Trigonometry Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the tangent of A. a. 0.6 c b. 0.8 d Find the sine of B. a. 0.6 c. 0.8 b d Find the cosine of A. a c. 0.8 b d

2 Name: 4. What is the length of AC? a c. 3 3 b. 3 d What is the length of BC? a c. 7 3 b. 3.5 d. 3 2

3 Name: 6. What is the length of AC? a. 2 c. 2 b. 2 2 d What is the length of AB? a. 2 c. 6 b. 6 2 d. 1 3

4 Name: 8. What is the width, w, of the lake shown below? a. 2.5 miles c. 2.4 miles b. 2.8 miles d. 3.5 miles 9. Solve the right triangle below. Round sides to the nearest thousandth and angles to the nearest degree. a. BC = , m A = 60, and m C = 30 b. BC = , m A = 60, and m C = 30 c. BC = , m A = 30, and m C = 60 d. BC = , m A = 30, and m C = 60 4

5 Name: 10. A newspaper reporter in a helicopter is taking pictures of a waterfall that is 150 meters tall. The helicopter is hovering 80 meters away from the waterfall and is level with the waterfall s tallest point. The reporter is focusing her camera on a point halfway down the waterfall. Approximate the angle of depression of the camera lens. a. 47 c. 62 b. 43 d A 11-foot ladder is placed against a wall. The ladder is on level ground at an angle of 74.5 to the horizontal. About how far up the wall will the top of the ladder be located? a ft c ft b ft d ft 5

6 Name: 12. Solve the right triangle below. a. AB = 14.4, m A= 35, and m C = 55 b. AB = 14.4, m A= 55, and m C = 35 c. AB = 20.2, m A= 55, and m C = 35 d. AB = 20.2, m A= 35, and m C = You see a hiker sitting on a bench taking a water break at the top of a hill at a 50 angle of elevation. Your eye level is 5 feet off the ground and you are standing 100 feet from the base of the hill. At what altitude is the hiker sitting on the bench? a. 84 ft c. 89 ft b. 124 ft d. 119 ft 14. A right triangle has one leg that measures 8 feet and another that measures 11 feet. Use sine, cosine, and/or tangent to find the measures of its acute angles. a. 27 and 63 c. 26 and 64 b. 36 and 54 d. 31 and The height of a tower is 75 meters. To the nearest degree, what is the angle of elevation of the sun when the tower casts a shadow that is 55 meters long? a. 54 b. It is not possible to determine the answer with the information given. c. 36 d A research ship is stationed in calm waters. The sonar detects a sunken ship at a depth of about 350 meters and a horizontal distance of 800 meters. What is the distance between the research ship and the sunken ship? What is the angle of depression to the sunken ship? a. 509 m and 64 c. 719 m and 26 b. 575 m and 66 d. 873 m and 24 6

7 Name: 17. The triangle below is isosceles. Calculate the sine, cosine, and tangent of X. a. sin X = 0.5, cos X = 0.8, and tan X = 0.8 b. sin X = 0.9, cos X = 0.5, and tan X = 1.6 c. sin X = 2, cos X = 1.1, and tan X = 0.6 d. sin X = 1.1, cos X = 2, and tan X = A right triangle has one leg that measures 11 feet and another that measures 21 feet. Use sine, cosine, and/or tangent to find the measures of its acute angles. a. 18 and 72 c. 23 and 67 b. 19 and 71 d. 28 and A tower is 93 meters high. At a bench, an observer notices the angle of elevation to the top of the tower is 35. How far is the observer from the base of the building? a. about 114 m c. about 65 m b. about 162 m d. about 133 m 7

8 Name: 20. Two monuments are 25 meters apart. The height of the shorter monument is 22 meters. The angle of elevation from the shorter monument to the taller monument is 40. What is the height of the taller monument? a. 43 m c. 30 m b. 55 m d. 61 m 8

9 North Carolina Math 2 Transition Edition Unit 5 Assessment: Trigonometry Answer Section MULTIPLE CHOICE 1. ANS: D PTS: 1 REF: MII 5.8 NAT: G-SRT.6 TOP: Exploring Trigonometric Ratios KEY: tangent right triangle trigonometric ratios 2. ANS: C PTS: 1 REF: MII 5.8 NAT: G-SRT.6 TOP: Exploring Trigonometric Ratios KEY: sine right triangle trigonometric ratios 3. ANS: D PTS: 1 REF: MII 5.8 NAT: G-SRT.6 TOP: Exploring Trigonometric Ratios KEY: cosine right triangle trigonometric ratios 4. ANS: A PTS: 1 REF: MII NAT: G-SRT.12 TOP: Trigonometry KEY: triangle right triangle special ratios tangent 5. ANS: B PTS: 1 REF: MII NAT: G-SRT.12 TOP: Trigonometry KEY: triangle right triangle special ratios sine 6. ANS: C PTS: 1 REF: MII NAT: G-SRT.12 TOP: Trigonometry KEY: triangle right triangle special ratios tangent 7. ANS: B PTS: 1 REF: MII NAT: G-SRT.12 TOP: Trigonometry KEY: triangle right triangle special ratios cosine 8. ANS: B PTS: 1 REF: MII 5.8 NAT: G-SRT.6 TOP: Exploring Trigonometric Ratios KEY: right triangle ratios application 9. ANS: B PTS: 1 REF: MII 5.9 NAT: G-SRT.8 KEY: right triangle arcsine arccosine arctangent Pythagorean Theorem complementary angles 10. ANS: B PTS: 1 REF: MII 5.9 NAT: G-SRT.8 KEY: right triangle arctangent trigonometry 11. ANS: B PTS: 1 REF: MII 5.9 NAT: G-SRT.8 KEY: right triangle sine trigonometry 1

10 12. ANS: A PTS: 1 REF: MII 5.9 NAT: G-SRT.8 KEY: right triangle sine cosine tangent complementary angles Pythagorean Theorem arcsine arccosine arctangent 13. ANS: B PTS: 1 REF: MII 5.9 NAT: G-SRT.8 KEY: right triangle tangent 14. ANS: B PTS: 1 REF: MII 5.9 NAT: G-SRT.8 KEY: right triangle sine cosine tangent complementary angles arcsine arccosine arctangent 15. ANS: A PTS: 1 REF: MII 5.9 NAT: G-SRT.8 KEY: right triangle tangent arctangent 16. ANS: D PTS: 1 REF: MII 5.9 NAT: G-SRT.8 KEY: right triangle tangent Pythagorean Theorem arctangent 17. ANS: B PTS: 1 REF: MII 5.9 NAT: G-SRT.8 KEY: isosceles triangle legs cosecant secant cotangent 18. ANS: D PTS: 1 REF: MII 5.9 NAT: G-SRT.8 KEY: right triangle sine cosine tangent complementary angles arcsine arccosine arctangent 19. ANS: D PTS: 1 REF: MII 5 NAT: G-SRT.8 TOP: Similarity, Right Triangle Trigonometry, and Proof KEY: right triangle trigonometry tangent MSC: Unit Assessment 20. ANS: A PTS: 1 REF: MII 5.9 NAT: G-SRT.8 KEY: right triangle tangent trigonometry 2