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Vectors in Trigonometry Practice Questions

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Updated on Oct 2, 2011

Read the following study guide for a concept review:

Vectors in Trigonometry Study Guide

Practice Questions

Find the endpoint of each vector if it starts at the origin.

1. length 70, angle 79°
2. length 30, angle 308°
3. length 68.4, angle 195.2°
4. length 400, 10° north of west
5. length 141, 21° west of south

 

Find the length and direction of the vector from the origin to the given point.

6. (–12,–3)
7. (2,7)
8. (23,–9)
9. (–208,119)
10. (1.926,–3.17)

 

Suppose the person in Figure 16.13 is trying to pull the heavy object with F pounds of force at an angle of θ from the horizontal. Find the component of the force that is going toward sliding the object across the floor.

Figure 16.13

11. θ = 20°, F = 150 pounds
12. θ = 5°, F = 80 pounds
13. θ = 60°, F = 200 pounds
14. θ = 37°, F = 180 pounds
15. θ = 8.6°, F = 130 pounds

Suppose a weight of W pounds is set on a ramp with angle θ, as illustrated in Figure 16.14. How much of the weight is going down the slope?

Figure 16.14

16. W = 100 pounds, θ = 15°
17. W = 200 pounds, θ = 18°
18. W = 40 pounds, θ = 42°
19. W = 1,000 pounds, θ = 5°
20. W = 100 pounds, θ = 87°
21. Suppose a person walks 30 meters north and then 44 meters northwest. What is the final distance and direction from the starting point?
22. A boat travels 14° north of east for 16 miles, and then 19° north of east for 20 miles. How far is the boat from where it started?
23. A hiker travels 25° south of west for 4 miles and then 10° north of west for 3 miles. In which direction should she head if she wants to go directly back to where she started?
24. A car is being driven through the desert. It goes for 12 miles in the direction 5° south of east. Then the car is turned and driven for 20 miles heading 7° north of east. Finally, it is driven for 9 miles heading 30° north of east. How far is it from where it started? In what direction is it from where it started?
25. Suppose two people are pulling on a heavy statue. One of them pulls with 180 pounds of force and the other with 120 pounds of force. The angle between the two people is 25°. With how much force is the statue being pulled in the direction of its movement? What is the direction of its movement?
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