Question

a ladder rests against the top of a wall. the head of a person is 5 feet 6 inches tall just touches the ladder. the person is 8 feet from the wall and 6 feet from the foot of the ladder. find the height of the wall. round your answer to the nearest whole number.

Answer 1

The wall and the person form two similar right triangles with respect to the foot of the ladder.

One characteristic of similar triangles is that the corresponding sides are at the same ratio.

This means that the ratio between the height of the person and the wall is equal to the ratio of the bases of both triangles.

$\frac{height.\text{wall}}{height.\text{person}}=\frac{\text{base wall}}{base\text{ person}}$

To make the calculations easier, I will write the height of the person in feet:

1in = 0.0833333..ft

6in=0.5 ft

5ft 6in =5.5ft

You can calculate the height of the wall as follows:

$\frac{x}{5.5}=\frac{14}{6}$

Multiply both sides by 5.5

$\begin{gathered} 5.5\cdot\frac{x}{5.5}=5.5\cdot\frac{14}{6} \\ x=12.8\bar{3}=13ft \end{gathered}$

The height of the wall is 13ft.