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 515 m away measures the angle of elevation to the spot of light to be 45°, as shown in the following figure.
515
A spotlight and an observer on horizontal ground, and a cloud above the ground, are shown.
The distance between the spotlight and the observer is 515 m.
A vertical dashed line labeled h connects the cloud to the ground at a right angle.
A second dashed line begins on the ground at the spotlight, goes up and left at an angle of 75° with the ground, and ends at the cloud.
A third dashed line begins at the observer, goes up and right at an angle of 45° with the ground, and ends at the cloud.
Find the height h of the cloud cover (in m). (Round your answer to the nearest meter.)
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