# Math Help - Height of a mt

1. ## Height of a mt

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

Is this problem able to be solved with out the law of sines? I can solve this problem if I use the law of sines and get the Hypotenuse, then use Cos(9)=y/hypot.

Thank you

2. let h = height of mountain

x = horizontal distance from final stop to a point directly beneath the mountain top

$\displaystyle \tan(3.5^\circ) = \frac{h}{x+13}
$

$\displaystyle \tan(9^\circ) = \frac{h}{x}$

solve the system for $h$

3. But that leaves me two variables still. So I will multiply both sides by x to get .1583844403x=h. When I do the law of sines I get 8.280294046 for the height.

4. Do I solve both for h and set each equal to one another again to find x then plug into equations to solve. Just been a while since had to do that. Law of sines easier. Thank you