Question

a woman wants to measure the height of a nearby building. she places a 10 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building. the total length of the building’s shadow is 165 ft, and the pole casts a shadow that is 4.25 ft long. how tall is the building? round your answer to the nearest foot. (the figure is not drawn to scale.)

Explanation:

Step1: Set up proportion

Let $h$ = height of building. The ratio of height to shadow length is equal for both objects:
$$\frac{h}{165} = \frac{10}{4.25}$$

Step2: Solve for $h$

Multiply both sides by 165 to isolate $h$:
$$h = \frac{10 \times 165}{4.25}$$

Step3: Calculate and round

Compute the value and round to nearest foot:
$$h = \frac{1650}{4.25} \approx 388.24 \approx 388$$

Answer:

388 ft