SOLUTION: 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

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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.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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%2Fsin%28110%29 = 10%2Fsin%2860%29
cross multiply
.866s = .9397*10
s = 9.397%2F.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%2F10.85
h = 10.85 * .17365
h = .32125 km or 321.25 meters high