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A pole that is 2.8m tall casts a shadow that is 1.15m long. At the same time, a nearby building casts a shadow that is 36.4m long. How tall is the building? Round your answer to the nearest meter.

User Alexey Romanov
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1 Answer

14 votes
14 votes

Explanation:

similar triangles.

each triangle is created by the object height, its shadow length, and the invisible distance between the top of the object and the end of the shadow.

in similar triangles the angles in both triangles are the same. and the ratio of sidelights of a pair of corresponding sides in both triangles is the same for every pair of corresponding sides.

so the ratio of the shadows of both objects must be the same as the ratio of the height of both objects.

36.4 / 1.15 = height / 2.8

height = 36.4 × 2.8 / 1.15 = 101.92 / 1.15 = 88.62608696...

so, rounded, the building is 89 meters tall.

User Thaum Rystra
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