Question

A pole that is 2.7 m tall casts a shadow that is 1.53 m long. At the same time, a nearby tower casts a shadow that is 42.25 m long. How tall is the tower? Round your answer to the nearest meter.

Answer 1

Answer:

The height of the tower is 75

Step-by-step explanation:

Given:

height of the pole = 2.7m

shadow of the pole = 1.53m

shadow of the tower = 42.25m

To find:

The height of the tower

To determine the height, we will apply the similarity theorem:

The ratio of corresponding sides will be equal

`\frac{shadow\text{ of pole}}{shadow\text{ of tower}}\text{ = }\frac{height\text{ of pole}}{height\text{ of tower}}`
`\begin{gathered} (1.53)/(42.25)=\frac{2.7}{height\text{ of the tower}} \\ \\ height\text{ of the tower = }\frac{42.25\text{ }*\text{ 2.7}}{1.53} \end{gathered}`
`\begin{gathered} height\text{ of the tower = 74.56 m} \\ \\ To\text{ the nearest meter, height of the tower is 75m} \end{gathered}`