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29 November, 13:59

A forest ranger in a 140-foot observation tower sees a fire moving in a direct path toward the windmill by the lake. The angle of depression to the fire is 3°, and the angle of depression to the windmill is 8°. To the nearest foot, how close is the fire to the windmill?

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  1. 29 November, 14:24
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    To get how close the windmill is to the fire we proceed as follows:

    distance from watch tower to the fire will be:

    tan θ = opposite/adjacent

    opposite=140 ft

    adjacent=x

    θ=3°

    hence

    tan 3=140/x

    x=140/tan 3

    x=2,671.36 ft

    the distance from watch tower to windmill will be:

    tan θ=opposite / adjacent

    θ=8°

    opposite=140 ft

    adjacent=y

    thus

    tan 8=140/y

    y=140/tan8

    y=999.15 ft

    the distance between fire and wind mill will be:

    2,671.36-999.15

    =1675.21~1675 ft (to the nearest ft)
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