A woman wants to measure the height of a nearby tower. She places a 10 ft pole in the shadow of the tower so that the shadow of the pole is exactly coveredby the shadow of the tower. The total length of the tower's shadow is 177 ft, and the pole casts a shadow that is 6.75 ft long. How tall is the tower? Round youranswer to the nearest foot. (The figure is not drawn to scale.)SunTowerlltх5?PoleShadow of poleShadow of tower

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AbagailR787482 AbagailR787482 · Answer 1 · 2022-10-28T16:54:28+02:00

262ft

Explanations:

From the given information, we have the following data:

• Height of the pole = 10ft

,

• Length of the tower's shadow = 177ft

,

• Length of the pole shadow = 6.75ft

Required

• Height of the tower (H)

To get the height of the tower, you will use the similarity theorem of triangles as shown:

[tex]\frac{Tower}{\text{shadow of tower}}=\frac{pole}{shadow\text{ of pole}}[/tex]

Substitute the given parameters into the formula to have:

[tex]\frac{\text{H}}{177}=\frac{10}{6.75}[/tex]

Cross multiply

[tex]\begin{gathered} 6.75H=177\times10 \\ 6.75H=1770 \\ H=\frac{1770}{6.75} \\ H=262.2ft \\ H\approx262\text{ft} \end{gathered}[/tex]

Therefore, the height of the tower to the nearest foot is 262ft