Question 725262
A motorist noticed that as he got 10 km closer to a mountain, the angle of elevation of the top of the mountain changed from 10 degrees to 70 degrees. 
Approximate the height of the mountain.
:
Draw this out, consider the triangle formed the by 10 km and the slant ranges from the two given points. 
The interior angles: 10, 180-70=110, and 60 degrees
Find the slant range(s) to the top of the mountain from initial position using the law of sines.
{{{s/sin(110)}}} = {{{10/sin(60)}}}
cross multiply
.866s = .9397*10
s = {{{9.397/.866}}}
s = 10.85 km to the top of the mountain
:
A right triangle where the side opposite is the height(h) of the mountain
sin(10) = {{{h/10.85}}}
h = 10.85 * .17365
h = .32125 km or 321.25 meters high