# Math

posted by Ashley

In traveling across flat land, you notice a mountain in front of you. Its angle of elevation to the peak is 3.5 degrees. After you drive 13 miles closer to the mountain, the angle of elevation is 9 degrees. Approximate the height of the mountain.

1. MathMate

Let the second observation be taken at x miles from the mountain.

Then
xtan(9°) = (13+x)tan(3.5°)
Solve for x after substituting the trig. ratios.
The height of the mountain is therefore
xtan(9°) miles
=5280 x tan(9°) ft.

2. Ashley

How do you figure it out from there though? Because I got that far and couldn't figure out how to solve for x.

3. MathMate

It's like solving for x in
ax=b(13+x)
x(a-b)=13b
x=13b/(a-b)

where
a=tan(9°)=0.158 approx.
b=tan(3.5°)=0.061 approx.

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