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Marta is standing 4 ft behind a fence 6 ft 6 in. tall. When she looks over the fence, she can just see the top edge of a building. She knows that the building is 32 ft 6 in. behind the fence. Her eyes are 5 ft from the ground. How tall is the building? Give your answer to the nearest half foot.

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tochjosh

Answer: 93ft

Explanation: Martha's eyesight make an angle with the fence, this is solved as a triangle problem.

We first convert all the dimensions to inches using the fact that 12 inches make 1 ft.

To solve for the angle

Tan § = 18/48 = 0.375

§ = tan^-1 of 0.375 = 20.55°

This same angle elevates to the edge of the building

Tan 20.55 = 399/x

x = 399/tan 20.55

x = 1040 inches

Height of building = x + height of fence

Height of building = 1040 + 78 = 1118 inches

Converting back to ft it becomes

1118/12 = 93 ft 2 inches

Approximately 93ft

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