Question 164379
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 75º, the angle at the observer is 45º, so the 3rd angle is 60º.
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