A pole that is 3.2m tall casts a shadow that is 1.59m long. At the same time, a nearby building casts a shadow that is 45.5m long. How tall is the building? Round your answer to the nearest meter.
Question
A pole that is 3.2m tall casts a shadow that is 1.59m long. At the same time, a nearby building casts a shadow that is 45.5m long. How tall is the building? Round your answer to the nearest meter.
Solution
To solve this problem, we can use the concept of similar triangles. The height of the pole and its shadow form one right triangle, and the height of the building and its shadow form another right triangle. The ratios of the corresponding sides of these triangles are equal.
Let's denote the height of the building as H.
We know that the height to shadow ratio of the pole is equal to the height to shadow ratio of the building. So we can write the equation:
3.2m (height of the pole) / 1.59m (shadow of the pole) = H (height of the building) / 45.5m (shadow of the building)
Solving this equation for H gives us:
H = 3.2m / 1.59m * 45.5m = 91.445m
Rounding to the nearest meter, the height of the building is approximately 91 meters.
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