Chapter 6, Problem 2E

To determine

To calculate:The height of tower when the shadow is $24$ feet long. At the same time, the height of mailbox is $4$ feet and shadow is $4$ feet long.

Answer to Problem 2E

The height of tower is $80$ feet.

Explanation of Solution

Given information:

Shadow of Tower $=24$ feet

Height of mailbox $=4$ feet

Shadow of mailbox $=1.2$ feet

Calculation:

Let the height of Towerbe $h$ .

Height to Shadowfractionsare as follows:

Fraction of mailbox $=\frac{4}{1.2}$$=\frac{40}{12}=\frac{10}{3}$

Fraction of Tower $=\frac{h}{24}$

Since, the height to shadow fractions are for the same time, comparing both the fractions−

  $\frac{10}{3}$$=\frac{h}{24}$

Solving the above equation, we have:

  $h=80$

Thus, the height of Tower is $80$ feet.