Question

a shadow 16 meters long is cast by a redwood tree that is 30 meters tall. what is the height of a nearby stone tower that casts a shadow 32 meters long? write your answer as a whole number or a decimal. do not round. meters

Explanation:

Step1: Set up the proportion

Since the ratio of height to shadow length is the same for both the tree and the tower, we can set up the proportion \(\frac{\text{height of tree}}{\text{shadow length of tree}}=\frac{\text{height of tower}}{\text{shadow length of tower}}\). Let \(h\) be the height of the tower. So, \(\frac{30}{16}=\frac{h}{32}\).

Step2: Solve for \(h\)

Cross - multiply: \(16h = 30\times32\). Then \(16h=960\). Divide both sides by 16: \(h=\frac{960}{16}\).

Answer:

\(60\)