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 couldn't 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(ab)=13b
x=13b/(ab)
where
a=tan(9°)=0.158 approx.
b=tan(3.5°)=0.061 approx.