Question

Valerie drives 400 meters up a hill that makes an angle of 20° with the horizontal. To the nearest tenth of a meter, what horizontal distance has she covered?
425.7 meters
375.9 meters
1169.5 meters
136.8 meters

Answer 1

Answer:

For this case we can model the problem as a rectangle triangle.

 We know:

 Length of the hypotenuse

 Angle between the base of the triangle and the hypotenuse.

 We want to know:

 Length of the base.

 For this we use the following trigonometric relationship:

 cos (15) = \frac{x}{500}cos(15)=500x

 Clearing x we have:

 x = 500 * cos (15) x = 482.96x=500∗cos(15)x=482.96

 Rounding to the nearest tenth of a meter:

 x = 483.0 mx=483.0m

 Answer:

 The horizontal distance she has covered is:

 x = 483.0 mx=483.0m