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A woman wants to measure the height of a nearby building. She places a 9ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building. The total length of the building shadow is 117ft, and the pole casts a shadow that is 6.5 ft long. How tall is the building? Round to the nearest foot.

A woman wants to measure the height of a nearby building She places a 9ft pole in the shadow of the building so that the shadow of the pole is exactly covered b class=

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ANSWER

[tex]162ft[/tex]

EXPLANATION

Let us make a sketch of the problem:

Let the height of the building be H.

The triangles formed by the shadows of the building and the pole are similar triangles.

In similar triangles, the ratios of the corresponding sides of the triangles are equivalent.

This implies that the ratio of the length of the shadow of the pole to the pole's height is equal to the ratio of the length of the shadow of the building to the building's height.

Hence:

[tex]\frac{6.5}{9}=\frac{117}{H}[/tex]

Solve for H by cross-multiplying:

[tex]\begin{gathered} H=\frac{117\cdot9}{6.5} \\ H=162ft \end{gathered}[/tex]

That is the height of the building.

Ver imagen TreborY66992