Question

4.2 independent practice
teks 7.5.a

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.
2. two ramps modeled with triangles are similar. which side of triangle koa corresponds to ( overline{j n} )? explain.

Explanation:

Step1: Set up proportion

Since the objects and their shadows form similar triangles, the ratios of height to shadow length are 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 the proportion

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

Answer:

\(9\) ft