SOLUTION:

Question 164379This question is from textbook
: This question is from textbook

Found 2 solutions by Alan3354, nottohave:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
To measure the height of the cloud cover at an airport, a worker shines a spotlight upward at an angle 75� from the horizontal. An observer at a distance D = 515 m away measures the angle of elevation to the spot of light to be 45�. Find the height h of the cloud cover, correct to the nearest meter.
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The angle from the light is 75�, the angle at the observer is 45�, so the 3rd angle is 60�.
Use the law of sines to find the distance "s" from the observer to the cloud:
515/sin(60) = s/sin(75)
s = 515*sin(75)/sin(60)
s = 574.41 meters
Then, the height is s*sin(45)
s = 406.17 meters

Answer by nottohave(4) (Show Source): You can put this solution on YOUR website!
Draw a normal triangle, angle from the light to the top is 75, other angle from observer to the top is 45. From the top straight to the bottom is 90 degree, and you got 2 right triangle. The height is h ( as you said ).
call x : adjacent side of 45 degree
515-x : the left over which next to 75 degree.
Then h= tan 45 (x) Also h = tan 75 ( 515-x)
That means: tan 45(x)= tan 75(515-x)
Solve x. Then plug x to the equa. tan 45(x) --> then you got h.
Good luck.