Question

a shadow 24 meters long is cast by a radio tower that is 45 meters tall. if a fir tree close by casts a shadow 32 meters long, how tall is the fir tree? write your answer as a whole number or a decimal. do not round. meters

Explanation:

Step1: Set up proportion

Let the height of the fir tree be \(x\). Since the ratio of height to shadow length is the same for both objects, we have \(\frac{45}{24}=\frac{x}{32}\).

Step2: Solve for \(x\)

Cross - multiply: \(24x = 45\times32\). Then \(x=\frac{45\times32}{24}\). Calculate \(45\times32 = 1440\), and \(1440\div24 = 60\).

Answer:

60