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25 September, 14:11

The shadow cast by a television tower is 171 ft 10 in. A pole that is stuck in the ground nearby has 2 ft sticking above the ground and casts a shadow that is 6 ft 3 in. in length. Based on this information, how high is the television tower?

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  1. 25 September, 16:15
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    the height is 54.99 ft or 659.84 in

    Step-by-step explanation:

    We know that the sides of similar triangles are proportional, so we can write:

    2 ft / 6 ft 3 in = x / 171 ft 10 in

    Now what we must do first and pass everything to the same unit of measurement:

    Knowing that 1 foot equals 12 inches:

    6 ft 3 in = 6 ft * 12 in / ft + 3 in = 72 + 3 = 75 in

    171 ft 10 in = 171 ft * 12 in / ft + 10 in = 2052 + 10 = 2062 in

    2 ft = 2 ft * 12 in / ft = 24 in

    replacing:

    24 in / 75 in = x / 2062 in

    x = 24 * 2062/75

    x = 659.84 in

    Or they would also be 659.84 in * 1 ft / 12 in = 54.99 ft

    That is, the height is 54.99 ft or 659.84 in
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