FILE No.63Unsolved
A man fell from a building, and police need to know the height of the fall. But the building plans cannot be found.
So they measured shadows at the same time, in the same place. An officer 6 ft tall casts a 9 ft shadow, and the building casts a 90 ft shadow. The sun is at the same height for both, and the ground is level.
At the same time of day, the ratio of shadow length to height is the same for every object.
How tall is the building?
If you get stuck, open the hints one at a time, in order.
How many times longer than the officer is the officer's shadow?
At the same time of day, the building's shadow is the same multiple of its height.
Divide 90 ft by that multiple.
How tall is the building?
Choose the answer closest to the truth.
60 ft
The answer is: 60 ft.
The officer is 6 ft tall and the shadow is 9 ft, so the shadow is 1.5 times the height. At the same time, the building's shadow is also 1.5 times its height. 90 / 1.5 = 60 ft.
As a proportion: 6 : 9 = height : 90, so height = 6 x 90 / 9 = 60. A nearby object of known size works as a measuring stick.
It seems impossible to get the height from a shadow alone, so the officer as a "ruler" is easy to overlook.
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