Question

A radio tower casts a shadow 8 feet long at the same time that a vertical yardstick casts a shadow half an inch long.How tall is the radio tower?

Answer 1

The height of radio tower is 576 feet approximately

Solution:

Given that, radio tower casts a shadow 8 feet long

At the same time that a vertical yardstick casts a shadow half an inch long

To find: height of radio tower

Let "x" be the height of radio tower

length of shadow of tower = 8 feet

Length of shadow of stick = $\frac{1}{2} \text{ inch}$

Convert inch to feet

$1 \text{ inch } = \frac{1}{12} \text{ foot }$

$\frac{1}{2} \text{ inch } = \frac{1}{2} \times \frac{1}{12} \text{ foot } = 0.0416 \text{ foot }$

Thus,

Length of shadow of stick = 0.0416 feet

Length of vertical yard stick = 3 feet (since 1 yard = 3 feet )

Therefore, by proportion we get,

$\frac{\text{ height of radio tower }}{ \text{ length of shadow of tower }}=\frac{\text{ Length of vertical yard stick}}{\text{ Length of shadow of stick }}$

Substituting the values we get,

$\frac{x}{8} = \frac{3}{0.0416}\\\\x = 8 \times 72.11\\\\x = 576$

Thus height of radio tower is 576 feet approximately