Question

1. a building casts a shadow 50 ft long, and a 5 ft pole casts a shadow 2 ft long. how can you calculate the height of the building? a. use the pythagorean theorem. b. set up a proportion using similar triangles. c. subtract the lengths of the shadows. d. compare the angles of elevation.

Explanation:

Step1: Identify similar - triangles concept

The situation forms similar right - angled triangles (the building and its shadow, the pole and its shadow).

Step2: Set up proportion

If we let the height of the building be $h$. The ratio of the height to the shadow length for the pole is the same as the ratio for the building. So, $\frac{h}{50}=\frac{5}{2}$.

Step3: Solve for $h$

Cross - multiply to get $2h = 5\times50$, then $h=\frac{250}{2}=125$ ft. The correct method is to set up a proportion using similar triangles.

Answer:

B. Set up a proportion using similar triangles.