Question

a tree that is 12 feet tall casts a shadow that is 9 feet long. at the same time, a nearby stop sign casts a shadow that is 6 feet long. what is the height, h, of the stop sign? a 4.5 ft b 7.3 ft c 8 ft d 9 ft

Explanation:

Step1: Set up proportion

Since the triangles formed by the objects and their shadows are similar, we can set up the proportion $\frac{height\ of\ tree}{length\ of\ tree's\ shadow}=\frac{height\ of\ stop - sign}{length\ of\ stop - sign's\ shadow}$, i.e., $\frac{12}{9}=\frac{h}{6}$.

Step2: Cross - multiply

Cross - multiplying gives us $9h = 12\times6$.

Step3: Solve for h

First, calculate $12\times6 = 72$. Then, $h=\frac{72}{9}=8$.

Answer:

C. 8 ft