A vertical stick and a vertical pole stand on level ground. At the same moment each casts a shadow, and the two right triangles formed by object, shadow and sunbeam are similar. The stick's triangle has area 1.2 m^2 and the pole's triangle has area 30 m^2, and the stick is 1.5 m tall. Find the height of the pole (in m).

Question

Accepted Answer

7.5. Area ratio pole : stick = 30/1.2 = 25, so the length ratio is √25 = 5. Pole height = 1.5 × 5 = 7.5 m. Using the area ratio 25 as the height factor gives 37.5 m, the commonest error here; 30 m just repeats the area figure and 6 m uses a factor of 4.

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