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A person whose eyes are 1.6 metres above the ground stands on one side of a...

A person whose eyes are 1.6 metres above the ground stands on one side of a still lake and observes the reflection of a 1.4 m tall fence on the opposite shore. His line of sight to the reflection of the top of the fence is 6.0o below the horizontal. How wide is the lake?

Answer: 29 metres

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Answer #1

distance of person from image on lake

tan 6 = 1.6 / x

x = 1.6 / tan 6 = 15.22 m

distance of fence from imge point on lake

tan 6 = 1.4 / y

y = 1.4 / tan 6 = 13.32 m

total width of lake

L = x + y = 28.5 ≈ 29 m

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