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A person 5.1 feet tall stands in line of a shadow cast from the top of the house. The shadow hits the top of the person's head, and continues until the shadow ends on the ground 2.7 feet from the person's shoes. The distance along the ground from the tip of the shadow to the house is 17.4 feet. Find the height of the house. Round your answer to one decimal place.

Respuesta :

Refer to the diagram shown below.

Let h =  the height of the house.
The two triangles ΔABC and ΔADE are similar because of AAA.
Therefore
[tex] \frac{DE}{BC} = \frac{AD}{AB}[/tex]
That is,
h/5.1 = 17.4/2.7 = 6.4444
Multiply each side by 5.1..
h = 5.1*6.4444 = 32.8664 ft

Answer: The height of the house is 32.9 ft (to 1 dec. pl.)
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