A person stands at a distance of 4.2 m from the pole on which a lantern hangs
| January 31, 2021 | education
A person stands at a distance of 4.2 m from the pole on which a lantern hangs, located at a height of 5 m. The shadow of a person is 2.8 m. How tall is a person?
Let us prove the similarity of right-angled triangles ABC and ADE.
Right-angled triangles ABC and ADE have a common angle A, and therefore right-angled triangles are similar in acute angle.
Determine the length of the leg AC of the right-angled triangle ABC.
AC = AE + CE = 2.8 + 4.2 = 7 m.
Since the triangles are similar, the ratio of their similar sides are equal, then:
AC / AE = BC / DE.
DE = AE * BC / AC = 2.8 * 5/7 = 2 m.
Answer: A person’s height is 2 m.
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