Question

indirect measurement
a man wants to measure the height of a nearby tower. he places a 6 ft pole in the shadow of the tower so that the shadow of the pole is exactly covered by the shadow of the tower. the total length of the tower’s shadow is 164 ft, and the pole casts a shadow that is 3.25 ft long. how tall is the tower? round your answer to the nearest foot. (the figure is not drawn to scale.)
shadow of pole
shadow of tower
ft

Explanation:

Step1: Set up proportion

Let \( h \) be the tower's height. The two right triangles (pole and its shadow, tower and its shadow) are similar, so \(\frac{6}{3.25}=\frac{h}{164}\).

Step2: Solve for \( h \)

Cross - multiply: \( 3.25h = 6\times164 \). Calculate \( 6\times164 = 984 \). Then \( h=\frac{984}{3.25}\approx302.77\). Round to nearest foot.

Answer:

303