A man with a height of 1.5 m stands 8 m from the post on which the lantern is fixed.

univerkov | June 10, 2021 | education

A man with a height of 1.5 m stands 8 m from the post on which the lantern is fixed. At what height is the lantern fixed if the length of the person’s shadow is 2 m?

Let us prove that right-angled triangles ABC and ADH are similar.

Angle A for triangles is common, then right-angled triangles are similar in acute angle.

Determine the length of the segment AC. AC = AH + CH = 2 + 8 = 10 m.

Then AC / AH = BC / DH.

BC = AC * DH / AH.

BC = 10 * 1.5 / 2 = 15/2 = 7.5 m.

Answer: The lantern is fixed at a height of 7.5 m.

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