Question

Valeria drives 500 meters up a hill that makes an angle of 15 degrees with the horizontal. To the nearest tenth of a meter, what horizontal distance has she covered?

Answer 1

Approximately 485 meters

Explanation:

We can first construct a right triangle, using the 500 m length of hill as our hypotenuse. Using the fact that the cosine of an angle is the ratio of the adjacent side to the hypotenuse, we see that

`cos(15^\circ)=(x)/(500)`

where x is the horizontal distance covered. Solving for x, we find this horizontal distance to be

`x=500cos(15^\circ)\approx500(0.97)=485`

so our answer is approximately 485 m.