The distance between the building and the base of the ladder is 5√3 feet.
Step-by-step 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 = [tex]\sqrt{hypotenuse^{2}-height^{2} }[/tex]
⇒ x = [tex]\sqrt{10^{2} -5^{2} }[/tex]
⇒ x = [tex]\sqrt{100-25}[/tex]
⇒ x = [tex]\sqrt{75}[/tex]
⇒ x = 5√3
The distance between the building and the base of the ladder is 5√3 feet.
