A woman wants to measure the height of a nearby building. She places a 9ft 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 199ft, and the pole casts a shadow that is 5.5ft long. How tall is the building? Round your answer to the nearest foot.
Question
A woman wants to measure the height of a nearby building. She places a 9ft 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 199ft, and the pole casts a shadow that is 5.5ft long. How tall is the building? Round your answer to the nearest foot.
Solution
This problem can be solved using similar triangles. The height of the building and its shadow form one triangle, and the height and shadow of the pole form a similar triangle.
The ratio of the height to the shadow length is the same for both triangles.
Let's denote the height of the building as H.
We know that the height to shadow ratio for the pole is 9ft/5.5ft = 1.63636 (rounded to 5 decimal places).
We also know that the total length of the building's shadow is 199ft.
So, we can set up the following equation to find the height of the building:
H/199ft = 1.63636
Solving for H gives us:
H = 199ft * 1.63636 = 325.75ft
Rounding to the nearest foot, the height of the building is approximately 326ft.
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