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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.

 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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