A woman wants to measure the height of a nearby tower. She places a 5 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 177 ft, and the pole casts a shadow that is 6.5 ft long. How tall is the tower? Round your answer to the nearest foot.

Question

Gianni Hodges

Mathematics

16 July, 20:48

A woman wants to measure the height of a nearby tower. She places a 5 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 177 ft, and the pole casts a shadow that is 6.5 ft long. How tall is the tower? Round your answer to the nearest foot.

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Cornelius Daniels · Answer 1

This scenario sets up a pair of similar right triangles. the smaller triangle had height 5 and base 6,5. the larger had height x (height of the tower, which we want to measure). and base of 177 the proportion is then x/177 = 5/6.5, or

6.5x = 5*177

6.5x=885

x=136.15

answer is 136 feet