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

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:
 [tex]cos (15) = \frac{x}{500} [/tex]
 Clearing x we have:
 [tex]x = 500 * cos (15) x = 482.96[/tex]
 Rounding to the nearest tenth of a meter:
 [tex]x = 483.0 m [/tex]
 Answer:
 The horizontal distance she has covered is:
 [tex]x = 483.0 m[/tex]