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9 July, 00:59

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 D = 510 m away measures the angle of elevation to the spot of light to be 45°. Find the height h of the cloud cover. (Round your answer to the nearest meter.)

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  1. 9 July, 01:20
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    Answer: The height of the cloud = 394.55 m

    Explanation:

    The observer is 500m away from the spotlight.

    Let x be the distance from the observer to the interception of the segment of the height, h with the floor. The equations are thus:

    Tan 45° = h/x ... eq1

    Tan 75° = h / (500 - x) ... eq2

    From eq 1, Tan 45° = 1, therefore eq1 becomes:

    h = x ... eq3

    Put eq3 into eq2

    Tan 75° = h / (500 - h)

    h = (500 - h) Tan 75°

    h = 500Tan 75° - hTan75°

    h + h Tan 75° = 500 Tan 75°

    h (1 + Tan 75°) = 500 Tan75°

    h = 500Tan75° / (1 + Tan 75°)

    h = 1866.02 / 4.73

    h = 394.55m
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