Posted by **Ashley** on Monday, November 22, 2010 at 5:43pm.

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.

- Math -
**MathMate**, Monday, November 22, 2010 at 5:59pm
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.

- Math -
**Ashley**, Monday, November 22, 2010 at 6:05pm
How do you figure it out from there though? Because I got that far and couldnt figure out how to solve for x.

- Math -
**MathMate**, Monday, November 22, 2010 at 11:31pm
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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