Question

Your geometry class goes outside to measure theheight of the school's flagpole. A student who is 5feet tall stands up straight and casts a shadow that is8 feet long. At the same time the flagpole casts ashadow that is 24 feet long. What is the height of theflagpole?

Answer 1

Hello there. To solve this question, we'll have to remember some properties about measuring heights and ratio.

A student who is 5 feet tall stands up straight and casts a shadow that is 8 feet long. At the same time, the flagpole casts a shadow that is 24 feet long. What is the height of the flagpole?

We start by drawing the situation:

In this case, we take the ratio between the heights and the shadow length. This must be a constant, equal to both.

Therefore we have to solve the following equation:

`(5)/(8)=(H)/(24)`

Multiply both sides of the equation by a factor of 24

`\begin{gathered} 24\cdot(5)/(8)=24\cdot(H)/(24) \\ H=15 \end{gathered}`

The height of the flagpole is 15 feet.