Question

a mountain casts a shadow of 120 meters. a 2 - meter pole beside it casts a shadow of 3 meters. what is the height of the mountain?

Explanation:

Step1: Set up the proportion

Since the ratio of height to shadow length is the same for both the pole and the mountain. Let the height of the mountain be \(h\). The proportion is \(\frac{h}{120}=\frac{2}{3}\).

Step2: Solve for \(h\)

Cross - multiply: \(3h = 2\times120\). Then \(3h=240\). Divide both sides by 3: \(h=\frac{240}{3}\).

Answer:

\(80\) meters