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Steve is buying a farm and needs to determine the height of a silo on the farm.Steve, who is 6 feet tall, notices that when his shadow is 12 ft long, the shadowof the silo is 180 ft long. How tall is the silo? Note that the diagram is not to scale.6 fs12 ft180 ftThe silo is ft tallTime Remaining: 00:58:13

Answer :

Given:

[tex]\begin{gathered} Steve\text{ height}(H_1)=6ft \\ Steve\text{ shadow}(S_1)=12ft \\ Silo^{\prime}s\text{ shadow}(S_2)=180ft \end{gathered}[/tex]

To Determine: The height of the silo

Solution

Let us compare the ratio of Steve's height and shadow with the height and shadow of the silo

[tex](H_2)=height\text{ of the silo}[/tex]

The ratio would be

[tex]\begin{gathered} \frac{H_1}{S_1}=\frac{H_2}{S_2} \\ \frac{6}{12}=\frac{H_2}{180} \end{gathered}[/tex]

Determine the height of the silo by cross-multiplying

[tex]\begin{gathered} 12H_2=6\times180 \\ H_2=\frac{6\times180}{12} \\ H_2=90ft \end{gathered}[/tex]

Hence, the silo is 90ft tall

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