Question

Paula leaned a 10 ft ladder against a building as shown below. if Paula wants the top of the ladder to reac

h exactly 5 feet up in the building, what is x the distance between the building and the base of the ladder, in feet?
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Answer 1

The distance between the building and the base of the ladder is 5√3 feet.

Explanation:

Consider a right angle triangle,

• Hypotenuse = Paula leaned a 10 ft ladder against a building.
• Height = the top of the ladder is exactly 5 feet up in the building.
• Base = 'x' ft, distance between the building and the base of the ladder.

From the Pythagorean theorem,

Base, x =
`\sqrt{hypotenuse^(2)-height^(2) }`

⇒ x =
`\sqrt{10^(2) -5^(2) }`

⇒ x =
`√(100-25)`

⇒ x =
`√(75)`

⇒ x = 5√3

The distance between the building and the base of the ladder is 5√3 feet.