A flagpole casts a shadow 16 feet long. Shanika is standing near the pole. Her shadow is 4 feet long. Shanika’s height is 5

Question

A flagpole casts a shadow 16 feet long.
Shanika is standing near the pole. Her
shadow is 4 feet long. Shanika’s height is 5
feet. How tall is the flagpole?

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Thiên Hương 3 years 2021-08-05T09:16:47+00:00 1 Answers 8 views 0

Answers ( )

    0
    2021-08-05T09:18:44+00:00

    Step-by-step explanation:

    Since Shanika is standing near the pole, we can safely assume that the triangle formed by Shanika and her shadow is a smaller version of the triangle formed by the pole and its shadow.

    By similar triangles:

     \frac{x \: of \: pole}{y \: of \: pole}  =  \frac{x \: of \: shanika}{y \: of \: shanika}  \\  \frac{16}{ height \: of \: pole}  =  \frac{4}{5}  \\ 16(5) = 4 \times height \: of \: pole \\  height \: of \: pole =  \frac{80}{4}  \\  = 20

    The height of the pole is 20ft.

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