Math 1201 Review Chapter 2

Transcription

1 Math 1201 Review hapter 2 Multiple hoice Identify the choice that best completes the statement or answers the question. 1. etermine tan Q and tan R. P 12 Q 16 R a. tan Q = ; tan R = 0.75 c. tan Q = 1.3; tan R = b. tan Q = 1.3; tan R = 0.75 d. tan Q = 0.75; tan R = etermine the measure of N to the nearest tenth of a degree. M 13 N 7 K a b c d alculate the angle of inclination, to the nearest tenth of a degree, of a road with a grade of 22%. a b c d etermine the measure of to the nearest tenth of a degree. 8 cm 19 cm a b c d Rhonda walked diagonally across a rectangular playground with dimensions 60 m by 45 m. She started at point. etermine the angle, to the nearest degree, between her path and the longest side of the playground.

2 45 m 60 m a. 37 b. 41 c. 53 d ladder leans against the side of a building. The top of the ladder is 5 m from the ground. The base of the ladder is 1.0 m from the wall. What angle, to the nearest degree, does the ladder make with the ground? a. 79 b. 11 c. 9 d etermine the tangent ratio for K. L M K a b c d etermine the length of side l to the nearest tenth of a metre. L 12.2 m M l 66 N a. 5.4 m b m c m d. 5.0 m 9. etermine the length of side s to the nearest tenth of a millimetre. R s T 20.3 mm 25 S a mm b mm c. 8.6 mm d. 9.5 mm 10. helicopter is ascending vertically. On the ground, a searchlight is 125 m from the point where the helicopter lifted off the ground. It shines on the helicopter and the angle the beam makes with the ground is 48. How high is the helicopter at this point, to the nearest metre?

3 a. 187 m b. 93 m c. 113 m d. 139 m 11. guy wire is attached to a tower at a point that is 5.5 m above the ground. The angle between the wire and the level ground is 56. How far from the base of the tower is the wire anchored to the ground, to the nearest tenth of a metre? a. 3.1 m b. 6.6 m c. 3.7 m d. 8.2 m 12. Terry is lying on the ground near the.. Legislature uilding. The angle between the ground and his line of sight to the highest point on the building is 53. The height of the building, from the ground to its highest point, is about 43 m. bout how far is Terry from a point on the ground vertically below the highest point on the building? Give the answer to the nearest metre. a. 71 m b. 57 m c. 34 m d. 32 m 13. road has an angle of inclination of 16. etermine the increase in altitude of the road, to the nearest metre, for every 150 m of horizontal distance. a. 523 m b. 144 m c. 43 m d. 41 m 14. surveyor held a clinometer 1.5 m above the ground from a point 60.0 m from the base of a tower. The angle between the horizontal and the line of sight to the top of the tower was 21. etermine the height of the tower to the nearest tenth of a metre. a m b m c m d m 15. etermine sin G and cos G to the nearest hundredth. F 84 E G a. sin G = 0.99; cos G = 6.54 c. sin G = 1.01; cos G = 0.15 b. sin G = 0.15; cos G = 0.99 d. sin G = 0.99; cos G = etermine the measure of Q to the nearest tenth of a degree.

4 P 7 Q 19 R a b c d helicopter is hovering 200 m above a road. car stopped on the side of the road is 300 m from the helicopter. What is the angle of elevation of the helicopter measured from the car, to the nearest degree? a. 56 b. 48 c. 42 d etermine the measure of X W Y to the nearest tenth of a degree Y a b c d ladder is 13.0 m long. It leans against a wall. The base of the ladder is 3.7 m from the wall. What is the angle of inclination of the ladder to the nearest tenth of a degree? a b c d rope that supports a canopy is 8.5 m long. The rope is attached to the canopy at a point that is 7.5 m above the ground. What is the angle of inclination of the rope to the nearest tenth of a degree? a b c d etermine the measure of to the nearest tenth of a degree.

5 25 17 a b c d etermine the length of XY to the nearest tenth of a centimetre. Y X cm Z a. 8.4 cm b cm c cm d cm 23. etermine the length of E to the nearest tenth of a centimetre. 7.7 cm E 29 F a. 8.8 cm b cm c. 3.7 cm d cm 24. From the start of a runway, the angle of elevation of an approaching airplane is t this time, the plane is flying at an altitude of 7.7 km. How far is the plane from the start of the runway to the nearest tenth of a kilometre? a. 8.1 km b. 2.3 km c km d km 25. surveyor made the measurements shown in the diagram. etermine the distance from R to S, to the nearest hundredth of a metre.

6 Q S m 56.5 R a m b m c m d m 26. guy wire is attached to a tower at a point that is 7.5 m above the ground. The angle of inclination of the wire is 67. etermine the length of the wire to the nearest tenth of a metre. a m b m c. 8.1 m d. 7.9 m 27. balloon is flying at the end of a 170-m length of string, which is anchored to the ground. The angle of inclination of the string is 50. alculate the height of the balloon to the nearest metre. a. 130 m b. 143 m c. 109 m d. 222 m 28. etermine the area of to the nearest square centimetre. R T 23.3 cm 21 S a. 291 cm 2 b. 707 cm 2 c. 104 cm 2 d. 208 cm Two trees are 55 yd. apart. From a point halfway between the trees, the angles of elevation of the tops of the trees are measured. What is the height of each tree to the nearest yard? tree tree yd. a. 33 yd.; 31 yd. c. 41 yd.; 50 yd. b. 19 yd.; 15 yd. d. 40 yd.; 49 yd. Short nswer 30. tree is supported by a guy wire. The guy wire is anchored to the ground 7.0 m from the base of the tree. The angle between the wire and the level ground is 60. How far up the tree does the wire reach, to the nearest tenth of a metre?

7 31. etermine the height of this isosceles triangle to the nearest tenth of a centimetre cm 32. Solve this right triangle. Give the measures to the nearest tenth. 9.1 cm F 26 E 33. etermine the length of WX to the nearest tenth of a centimetre. W 9.5 cm 29 Z X 31 Y 34. alculate the measure of to the nearest degree. 10 cm 9 cm 13 cm 35. From the top of an 80-ft. building, the angle of elevation of the top of a taller building is 49 and the angle of depression of the base of this building is 62. etermine the height of the taller building to the nearest foot.

8 ft. 36. alculate the measure of to the nearest tenth of a degree. 13 cm 7 cm 4 cm 37. etermine the length of RS to the nearest tenth of a centimetre. R Q 8.9 cm 54 S 39 T Problem 38. In the diagram below, a oast Guard patrol boat is at, which is 11.7 km south of Point tkinson lighthouse. sailboat in distress is at, which is 7.3 km west of the lighthouse. a) How far is the patrol boat from the sailboat, to the nearest tenth of a kilometre? b) t what angle to should the patrol boat travel to reach the sailboat? Give the answer to the nearest tenth of a degree.

9 7.3 km 11.7 km 39. etermine the measures of and to the nearest tenth of a degree Three squares with side length 9 mm are placed side-by-side as shown. Thomas says is approximately a) Is he correct? Justify your answer. b) escribe what the value of tan indicates. G 9 mm E 41. guy wire is connected from a tower to the ground. etermine the height of the tower, to the nearest tenth of a metre. What assumptions about the ground are you making? 49 E 30.1 m 42. The angle between one longer side of a rectangle and a diagonal is 37. One shorter side of the rectangle is 6.2 cm.

10 a) Sketch and label the rectangle. b) What is the length of the rectangle to the nearest tenth of a centimetre? 43. etermine the area of to the nearest tenth of a square unit. etermine its perimeter to the nearest tenth of a unit boat was docked 30.0 m from the base of a cliff. sailor used a clinometer to sight the top of the cliff. The angle between the horizontal and the line of sight was 74. The sailor held the clinometer 1.5 m above the surface of the water. etermine the height of the cliff to the nearest tenth of a metre. 45. alculate the angle of inclination of the roof to the nearest tenth of a degree. 12 ft. rafters 22 ft. 46. etermine the measures of and to the nearest tenth of a degree etermine the area of this right triangle to the nearest square metre.

11 L 850 m M 57 N 48. etermine the perimeter of this triangle to the nearest tenth of a centimetre. \ 9.0 cm / Solve XYZ. Give the measures to the nearest tenth. Explain your strategy. X Y 18.9 cm 45 Z 50. etermine the area of this triangle to the nearest tenth of a square centimetre cm 129

12 Math 1201 Review hapter 2 nswer Section MULTIPLE HOIE 1. NS: PTS: 1 IF: Easy REF: 2.1 The Tangent Ratio 2. NS: PTS: 1 IF: Easy REF: 2.1 The Tangent Ratio 3. NS: PTS: 1 IF: Moderate REF: 2.1 The Tangent Ratio 4. NS: PTS: 1 IF: Moderate REF: 2.1 The Tangent Ratio 5. NS: PTS: 1 IF: Easy REF: 2.1 The Tangent Ratio 6. NS: PTS: 1 IF: Moderate REF: 2.1 The Tangent Ratio 7. NS: PTS: 1 IF: Moderate REF: 2.1 The Tangent Ratio 8. NS: PTS: 1 IF: Easy REF: 2.2 Using the Tangent Ratio to alculate Lengths LO: 10.M4 TOP: Measurement KEY: Procedural Knowledge 9. NS: PTS: 1 IF: Easy REF: 2.2 Using the Tangent Ratio to alculate Lengths LO: 10.M4 TOP: Measurement KEY: Procedural Knowledge 10. NS: PTS: 1 IF: Moderate REF: 2.2 Using the Tangent Ratio to alculate Lengths LO: 10.M4 TOP: Measurement KEY: Procedural Knowledge 11. NS: PTS: 1 IF: Moderate REF: 2.2 Using the Tangent Ratio to alculate Lengths LO: 10.M4 TOP: Measurement KEY: Procedural Knowledge 12. NS: PTS: 1 IF: Moderate REF: 2.2 Using the Tangent Ratio to alculate Lengths LO: 10.M4 TOP: Measurement KEY: Procedural Knowledge 13. NS: PTS: 1 IF: Moderate REF: 2.2 Using the Tangent Ratio to alculate Lengths LO: 10.M4 TOP: Measurement KEY: Procedural Knowledge 14. NS: PTS: 1 IF: Easy REF: 2.3 Math Lab: Measuring an Inaccessible Height LO: 10.M4 TOP: Measurement KEY: Procedural Knowledge 15. NS: PTS: 1 IF: Easy REF: 2.4 The Sine and osine Ratios 16. NS: PTS: 1 IF: Easy REF: 2.4 The Sine and osine Ratios 17. NS: PTS: 1 IF: Moderate REF: 2.4 The Sine and osine Ratios 18. NS: PTS: 1 IF: Easy REF: 2.4 The Sine and osine Ratios

13 19. NS: PTS: 1 IF: Moderate REF: 2.4 The Sine and osine Ratios 20. NS: PTS: 1 IF: Moderate REF: 2.4 The Sine and osine Ratios 21. NS: PTS: 1 IF: Easy REF: 2.4 The Sine and osine Ratios 22. NS: PTS: 1 IF: Easy REF: 2.5 Using the Sine and osine Ratios to alculate Lengths 23. NS: PTS: 1 IF: Moderate REF: 2.5 Using the Sine and osine Ratios to alculate Lengths 24. NS: PTS: 1 IF: Moderate REF: 2.5 Using the Sine and osine Ratios to alculate Lengths 25. NS: PTS: 1 IF: Easy REF: 2.5 Using the Sine and osine Ratios to alculate Lengths 26. NS: PTS: 1 IF: Easy REF: 2.5 Using the Sine and osine Ratios to alculate Lengths 27. NS: PTS: 1 IF: Easy REF: 2.5 Using the Sine and osine Ratios to alculate Lengths 28. NS: PTS: 1 IF: Moderate REF: 2.6 pplying the Trigonometric Ratios LO: 10.M4 TOP: Measurement KEY: Procedural Knowledge 29. NS: PTS: 1 IF: Easy REF: 2.7 Solving Problems Involving More than One Right Triangle SHORT NSWER 30. NS: 12.1 m PTS: 1 IF: Moderate REF: 2.2 Using the Tangent Ratio to alculate Lengths 31. NS: 23.4 cm PTS: 1 IF: ifficult REF: 2.5 Using the Sine and osine Ratios to alculate Lengths 32. NS: EF = 18.7 cm F = 20.8 cm = 64.0

14 PTS: 1 IF: Easy REF: 2.6 pplying the Trigonometric Ratios 33. NS: 16.1 cm PTS: 1 IF: Moderate REF: 2.7 Solving Problems Involving More than One Right Triangle 34. NS: 94 PTS: 1 IF: Easy REF: 2.7 Solving Problems Involving More than One Right Triangle 35. NS: 129 ft. PTS: 1 IF: Moderate REF: 2.7 Solving Problems Involving More than One Right Triangle 36. NS: PTS: 1 IF: Moderate REF: 2.7 Solving Problems Involving More than One Right Triangle 37. NS: cm PTS: 1 IF: Easy REF: 2.7 Solving Problems Involving More than One Right Triangle PROLEM 38. NS: a) Use the Pythagorean Theorem in right. The oast Guard patrol boat is approximately 13.8 km from the sailboat.

15 b) Use the tangent ratio in right. The patrol boat should travel at an angle of approximately 32.0 to to reach the sailboat. PTS: 1 IF: Moderate REF: 2.1 The Tangent Ratio LO: 10.M4 TOP: Measurement KEY: Problem-Solving Skills 39. NS: etermine the measure of in right. etermine the measure of. PTS: 1 IF: Moderate REF: 2.1 The Tangent Ratio LO: 10.M4 TOP: Measurement KEY: Problem-Solving Skills 40. NS: a) = mm In right :

16 Thomas is correct. b) In above, tan indicates that the length of the side opposite adjacent to. is 3 times the length of the side PTS: 1 IF: Moderate REF: 2.1 The Tangent Ratio LO: 10.M4 TOP: Measurement KEY: ommunication Problem-Solving Skills 41. NS: In right E, side E is opposite and E is adjacent to. Solve the equation for E. The height of the tower is approximately 26.2 m. I am assuming the ground is horizontal. PTS: 1 IF: Moderate REF: 2.2 Using the Tangent Ratio to alculate Lengths

17 LO: 10.M4 TOP: Measurement KEY: ommunication Problem-Solving Skills 42. NS: a) 6.2 cm 37 b) In right, is opposite and is adjacent to. Solve the equation for. The length of the rectangle is approximately 8.2 cm. PTS: 1 IF: Moderate REF: 2.2 Using the Tangent Ratio to alculate Lengths LO: 10.M4 TOP: Measurement KEY: Problem-Solving Skills 43. NS: etermine the length of. In right, is opposite and is adjacent to. Solve the equation for.

18 Find the area of. The area of is approximately square units. etermine the length of. Use the Pythagorean Theorem in right. The perimeter of is: The perimeter of is approximately units. PTS: 1 IF: ifficult REF: 2.2 Using the Tangent Ratio to alculate Lengths LO: 10.M4 TOP: Measurement KEY: Problem-Solving Skills 44. NS: Sketch and label a diagram to represent the information in the problem. In right, is opposite and is adjacent to. Solve this equation for m 1.5 m

19 Find the height, h, of the cliff. The height of the cliff is approximately m. PTS: 1 IF: Moderate REF: 2.3 Math Lab: Measuring an Inaccessible Height LO: 10.M4 TOP: Measurement KEY: Problem-Solving Skills 45. NS: raw a diagram to represent the cross-section of the roof. Find. 12 ft. In right : 11 ft. The angle of inclination of the roof is approximately PTS: 1 IF: Moderate REF: 2.4 The Sine and osine Ratios LO: 10.M4 TOP: Measurement KEY: Problem-Solving Skills 46. NS: etermine the measure of first. In right :

20 is approximately 61.4 and is approximately PTS: 1 IF: Moderate REF: 2.4 The Sine and osine Ratios LO: 10.M4 TOP: Measurement KEY: Problem-Solving Skills 47. NS: In right LMN, LN is the hypotenuse, LM is opposite N, and MN is adjacent to N. Use the sine ratio to determine the height of the triangle, LM. Solve this equation for LM. Use the cosine ratio to determine the length of MN, the base of the triangle. Solve this equation for MN.

21 Use the formula for the area,, of a triangle. The area of the triangle is approximately m. PTS: 1 IF: ifficult REF: 2.5 Using the Sine and osine Ratios to alculate Lengths LO: 10.M4 TOP: Measurement KEY: Problem-Solving Skills 48. NS: In right, is the hypotenuse, is opposite, and is adjacent to. To determine the length of, use the sine ratio. Solve this equation for. To determine the length of, use the cosine ratio. Solve this equation for.

22 Since = and =, the perimeter, P, of the triangle is: he perimeter of the triangle is approximately 58.9 cm. PTS: 1 IF: ifficult REF: 2.5 Using the Sine and osine Ratios to alculate Lengths LO: 10.M4 TOP: Measurement KEY: Problem-Solving Skills 49. NS: The acute angles in a right triangle have a sum of 90. In right XYZ: etermine the length of XY. Since XY is opposite Z and YZ is adjacent to Z, use the tangent ratio. XY is approximately 18.9 cm. etermine the length of XZ. Since YZ is adjacent to Z and XZ is the hypotenuse, use the cosine ratio.

23 XZ is approximately 26.7 cm. PTS: 1 IF: Moderate REF: 2.6 pplying the Trigonometric Ratios LO: 10.M4 TOP: Measurement KEY: ommunication Problem-Solving Skills 50. NS: Label a diagram. is an isosceles triangle, so each base angle is: 22.1 cm 129 etermine the height,, of the triangle. In right, is opposite and is the hypotenuse. So, use the sine ratio in etermine the length of the base,, of = 2() In right, is adjacent to and is the hypotenuse. So, use the cosine ratio in.

24 The base,, is: The formula for rea,, of a triangle is: The area of the triangle is approximately cm 2. PTS: 1 IF: ifficult REF: 2.7 Solving Problems Involving More than One Right Triangle LO: 10.M4 TOP: Measurement KEY: Problem-Solving Skills