Question

1. take it further suppose you want to find the height of a flagpole. you know your height. you can measure the length of the shadow of the flagpole. your friend can measure your shadow. how can you use ratios to find the height of the flagpole? explain. include a sketch in your explanation.

Explanation:

Step1: Set up the proportion

Let your height be $h_1$, the length of your shadow be $s_1$, the height of the flag - pole be $h_2$ and the length of the flag - pole's shadow be $s_2$. Since the ratio of height to shadow length is the same for both you and the flag - pole (because the angle of the sun is the same for both), we have the proportion $\frac{h_1}{s_1}=\frac{h_2}{s_2}$.

Step2: Solve for the flag - pole height

We can cross - multiply the proportion to get $h_2=\frac{h_1\times s_2}{s_1}$. We know $h_1$, $s_1$ and $s_2$ (by measurement), so we can calculate $h_2$.

For the sketch: Draw two vertical lines, one to represent you and one to represent the flag - pole. Draw horizontal lines from the bottom of each vertical line to represent the shadows. The angle between the top of the vertical line and the end of the shadow line is the same for both (the angle of the sun's rays).

Answer:

Set up the proportion $\frac{h_1}{s_1}=\frac{h_2}{s_2}$ and solve for $h_2$ as $h_2 = \frac{h_1\times s_2}{s_1}$, where $h_1$ is your height, $s_1$ is the length of your shadow, $h_2$ is the height of the flag - pole and $s_2$ is the length of the flag - pole's shadow.