At what distance in meters from the lantern is a person standing 1.6 meters tall, the length
| June 10, 2021 | education
At what distance in meters from the lantern is a person standing 1.6 meters tall, the length of his shadow is 8 meters, and the height of the lantern is 5 meters?
In right-angled triangles ABC and ADE, the angle A is common, then these triangles are similar in acute angle.
Let the length of the segment EC = X cm, then the length of the segment AC = (AE + EC) = (8 + X) cm.
From the similarity of triangles it follows: AC / AE = BC / DE.
(8 + X) / 8 = 5 / 1.6.
8 + X = 40 / 1.6 = 25.
X = EC = 25 – 8 = 17 m.
Answer: A man stands at a distance of 17 meters from the lantern.
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