A 2m tall man stands 3.5m away from a street lamp, and his shadow is 1m long.
| September 16, 2021 | education
A 2m tall man stands 3.5m away from a street lamp, and his shadow is 1m long. Determine the height of the lantern (in m.).
Determine the length of the segment AD. AD = AK + DK = 1 + 3.5 = 4.5 m.
Let us prove that triangle ACD is similar to triangle ABK.
Both triangles are straight, since CD and BK are perpendicular to AD, and the angle A is common for the triangles, then the triangles ACD and ABK are similar in acute angle.
CD / BK = AD / AK.
CD / 2 = 4.5 / 1.
1 * CD = 2 * 4.5.
CD = 4.5 m.
Answer: The height of the lantern is 4.5 meters.
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