A roofer needs to repair some shingles on the roof of a house, and uses a 12 foot ladder to reach the roof. In order to clear the bushes, th

Question

A roofer needs to repair some shingles on the roof of a house, and uses a 12 foot ladder to reach the roof. In order to clear the bushes, the roofer puts the ladder 5 feet out from the side of the house. What is the height of the house from the ground to the beginning of the roof?

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2 weeks 2022-01-12T02:37:31+00:00 1 Answer 0 views 0

1. The height of the house from the ground to the beginning of the roof is about 10.92 feet

Step-by-step explanation:

In a right triangle, the relation between the hypotenuse and the two legs of it is c² = a² + b², where

• a and b are the legs of the right angle
• c is the hypotenuse

In the problem the ladder, the height of the house and the distance between the ladder and the height of the house formed a right triangle where the ladder is its hypotenuse, the height of the house and the distance between the base of the house and the base of the ladder are the legs of it

∵ The ladder is 12 feet

∴ c = 12

∵ The roofer puts the ladder 5 feet out from the side of the house

∴ a = 5

– We need to find the height of the house so let b represents

the height of house

∴ b = the height of the house

– By using the relation above

(12)² = (5)² + b²

∴ 144 = 25 + b²

– Subtract 25 from both sides

∴ 119 = b²

– Take √ for both sides

10.91 ≅ b

The height of the house from the ground to the beginning of the roof is about 10.92 feet