Question

a pole that is 2.7 m tall cast a shadow that is 1.5 m long. at the same time, a nearby tower casts a shadow that is 40.7 m long. how tall is the tower? round to nearest meter

Answer 1

Similar Triangles

Both the pole and the tower and their respective shadows form similar triangles assuming the measurements are done at the very same time.

Similar triangles have the property that their respective sides have the same ratio, i.e., they are in the same proportion, thus:

`\frac{height\text{ of the tower}}{shadow\text{ of the tower}}=\frac{\text{height of the pole}}{shadow\text{ of the pole}}`

Solving for the height of the tower (H):

`height\text{ of the tower}=shadow\text{ of the tower}\cdot\frac{\text{height of the pole}}{shadow\text{ of the pole}}`

The problem gives the following data:

Height of the pole = 2.7 m

Shadow of the pole = 1.5 m

Shadow of the tower = 40.7 m

Substituting the values, we have:

`\begin{gathered} H=40.7\cdot(2.7)/(1.5) \\ H=73.26 \end{gathered}`

The tower is 73 m tall