At what distance from the lamp does a person stand 1.8 m tall, if the length of his shadow is 9 m, the height of the lamp is 5 m

bystudin | May 31, 2020 | Education

Consider the triangles ABC and DCE, these triangles are similar, because ∠C is common, ∠B and ∠DEC are straight, and the angles A and EDC are equal, as they are corresponding.
It follows from the similarity of these triangles that AB / DE = BC / EC, AB / DE = (BE + EC) / EC, hence (AB * EC) / DE = BE + EC
BE = (AB * EC) / DE-EC
BE = (5 * 9) / 1.8-9 = 16
Answer: the distance from the lamp to the person is 16 m

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