Question

Your geometry class is standing outside to measure the height of the school's flagpole. Astudent who is 5 feet tall stands and casts a shadow that is 9 feet long. At the same time theflagpole casts a shadow that is 28 feet long. What is the height of the flagpole?

Answer 1

The flagpole casts a shadow that is 28ft long, at the same time, a student with a height of 5ft casts a 9ft long shadow.

The flagpole and its shadow form a right triangle, the same happens with the height of the student and the shadow he cast, both triangles are similar:

If both triangles are similar, then their corresponding sides are at the same ratio, so that:

`(x)/(5)=(28)/(9)`

From this expression you can determine the height of the flagpole, multiply both sides of the equal sign by 5:

`\begin{gathered} 5\cdot(x)/(5)=5\cdot(28)/(9) \\ x=(140)/(9) \\ x\cong15.56ft \end{gathered}`

The flagpole has an approximate height of 15.56ft