SOLUTION: An observer at the foot of a hill notes that the angle of elevation of the top of the hill is 50 degrees. He walks 500 metres towards its summit along a slope inclined at an angle

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Question 921064: An observer at the foot of a hill notes that the angle of elevation of the top of the hill is 50 degrees. He walks 500 metres towards its summit along a slope inclined at an angle of 30 degrees, and then finds that the angle of elevation of the top of the hill is 75 degrees. Calculate the height of the hill, giving your answer to 3 significant figures. Draw a diagram
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
F = Foot of the hill, T = Top of the hill, M = point 500 meters up the hill
(The observer walks from F to M.)
Horizontal and vertical imaginary lines are blue.
Lines of sight to the top are green.
Here are my diagrams:
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The first diagram allows us to figure out the angles for the second diagram.
The second diagram and the law of sines allow us to find the length of FT.
FT%2Fsin%28135%5Eo%29=500%2Fsin%2825%5Eo%29
FT%2F0.7071=500%2F0.4226
FT=0.7071%2A500%2F0.4226
FT=836.6
The third diagram and the length of FT allow us to find height blue%28h%29 .
h=FT%2Asin%2850%5Eo%29
h=836.6%2A0.7660
highlight%28h=641%29 (rounded to 3 significant figures).
The height of the hill (rounded to 3 significant figures) is highlight%28641%29 meters.