Question

1. a cactus casts a shadow that is 15 ft long. a gate nearby casts a shadow that is 5 ft long. find the height of the cactus.

Explanation:

Step1: Set up proportion

Since the objects and their shadows form similar triangles, the ratio of height to shadow length is equal. Let \(x\) be the height of the cactus. The proportion is \(\frac{\text{height of gate}}{\text{shadow of gate}}=\frac{\text{height of cactus}}{\text{shadow of cactus}}\), so \(\frac{3}{5}=\frac{x}{15}\).

Step2: Solve for \(x\)

Cross - multiply: \(5x = 3\times15\). Then \(5x=45\). Divide both sides by \(5\): \(x=\frac{45}{5}\).

Answer:

\(9\) ft