A man 1.8 m in height stands at a distance of 8 m from a pole, on top of which a lantern weighs.
| August 13, 2021 | education
A man 1.8 m in height stands at a distance of 8 m from a pole, on top of which a lantern weighs. Find the height of the pillar if the length of the shadow cast by these people is 1.8 m
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 = 1.8 + 8 = 9.8 m.
Since the triangles are similar, the ratio of their similar sides are equal, then:
AC / AE = BC / DE.
BC = AC * DE / AE = 9.8 * 1.8 / 1.8 = 9.9 m.
Answer: The height of the pillar is 9.8 meters.
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