Question

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?

Answer 1

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

Answer 2

Applying the soh cah toa principle, we found the horizontal distance to be

482.95 meters

Mensuration of Flat Shapes(Triangle)

Given Data

• Distance driven Hyp = 500 meters

• Angle of elevation = 15°

• Horizontal Distance Adj= ??

Applying the SOH CAH TOA

Cos Ф = Adj/Hyp

Cos 15 = Adj/500

Adj = 0.9659*500

Adj = 482.95

Hence the horizontal distance is 482.95 meters

Learn more about triangles here:

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