A man wants to measure the height of a nearby tower. He places a 6ft 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 198ft, and the pole casts a shadow that is 4.25ft long. How tall is the tower? Round your answer to the nearest foot.
Question
A man wants to measure the height of a nearby tower. He places a 6ft 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 198ft, and the pole casts a shadow that is 4.25ft long. How tall is the tower? Round your answer to the nearest foot.
Solution
This problem can be solved using similar triangles. The ratio of the height to the shadow length is the same for both the pole and the tower.
- First, we set up the ratio for the pole: height/shadow = 6ft/4.25ft.
- Then, we set up a similar ratio for the tower: height/shadow = x (the unknown height of the tower we're trying to find)/198ft.
- Since the ratios are equal, we can set them equal to each other and solve for x: (6ft/4.25ft) = x/198ft.
- Cross-multiplying gives us: 4.25x = 1188.
- Solving for x gives us: x = 1188 / 4.25 = approximately 280ft.
So, the tower is approximately 280 feet tall.
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