Question

a man wants to measure the height of a nearby building. he places a 6 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 buildings shadow is 173 ft, and the pole casts a shadow that is 5.25 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

Since the triangles are similar (due to the same sun - angle), the ratio of height to shadow length is the same for the pole and the building. Let \(h\) be the height of the building. The proportion is \(\frac{\text{height of pole}}{\text{shadow of pole}}=\frac{\text{height of building}}{\text{shadow of building}}\). The height of the pole is \(6\) ft, the shadow of the pole is \(5.25\) ft, and the shadow of the building is \(173\) ft. So, \(\frac{6}{5.25}=\frac{h}{173}\).

Step2: Solve for \(h\)

Cross - multiply: \(5.25h = 6\times173\). First, calculate \(6\times173 = 1038\). Then, \(h=\frac{1038}{5.25}\).

Step3: Calculate the value of \(h\)

\(h=\frac{1038}{5.25}=\frac{1038\times100}{5.25\times100}=\frac{103800}{525}\approx198\) (rounded to the nearest foot).

Answer:

\(198\)