Question

Im not the best at word problems Jeff was curious about the height of the Al Hamra Tower and decided to measure it indirectly while he was in Kuwait City, Kuwait. He used a 2-meter model of the building that he found in a gift shop and measured the length of the shadow of the model to be 2.4 meters. Then he measured the length of the shadow of the Al Hamra Tower and found it to be 492 meters. What is the height of the Al Hamra Tower?

Answer 1

Assuming that he measured both the model and the tower at the same time of the day (this is important because the length of the shadow varies as the sum moves, causing the calculations to be inaccurate).

The height of the model and the length of its shadow form a right triangle, the same happens with the height of the tower and its shadow. Since both shadows were measured at the same time of the day, you can consider both right triangles to be similar:

The fact that both triangles are similar indicates that the ratio between the corresponding sides is equal. This means that the ratio between the shadow lengths is equal to the ratio between the heights of the actual tower and the model, you can express them as follows:

`\frac{\text{tower}}{\text{model}}=(492)/(2.4)=(x)/(2)`

From this expression, you can determine the height of the tower:

`\begin{gathered} (492)/(2.4)=(x)/(2) \\ 205=(x)/(2) \end{gathered}`

Multiply both sides by 2:

`\begin{gathered} 205\cdot2=2\cdot(x)/(2) \\ 410=x \end{gathered}`

The height of the Al Hamra tower is 410 meters.