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.
| 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?
| 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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