Question

Two flagpoles stand side by side. The first flagpole is 50 feet tall. The second flagpole is as tall as the first flagpole's shadow is long. The second flagpole's shadow is 18 feet long. How many feet tall is the second flagpole?

Answer 1

Answer: The second flagpole is 30 ft tall.

Step-by-step explanation: The two poles and their shadows form proportional right triangles.

The first pole's shadow is as long as the second pole is tall, which means that the length of the shadow and the height of the pole are equal and will be called x.

The figure in the attachment shows those proportions.

The proportions are:

$\frac{50}{x} = \frac{x}{18}$

x² = 50.18

x² = 900

x = ± $\sqrt{900}$

x = ± 30

Since x is a measurement, we take the positive value.

So, the second flagpole is 30 ft tall.

Answer 2

      |            |
50 |         x |
      |____   |______ 
           x           18

x = 30
50 * .6 = 30
30 * .6 = 18