Question

a painter has a 24-foot ladder that he is using to paint a house. for safety reasons, the ladder must be placed at least 8 feet from the base of the side of the house. to the nearest tenth of a foot , how high can the ladder safety reach?

Answer 1

The Pythagorean Theorem states that: "the sum of the squares of the legs is equal to the square of the hypotenuse."
a² + b² = c² or c² = a² + b²

Note¹: Hypotenuse is the side opposite the right angle.
Note²: The legs are the sides that are not opposite the right angle.
Note³: The sloping ladder leaning against the side of the house forms a right angle.

Solving

Data:
c = 24 ft
a = 8 ft
b = ?

Solving:

`c^2 = a^2 + b^2`

`24^2 = 8^2 + b`

`576 = 64 + b^2`

`b^2 = 576 - 64`

`b^2 = 512`

`b = √(512)`

`b = 22.627417 \to \boxed{\boxed{b \approx 22.6}}\end{array}}\qquad\quad\checkmark`

Answer:
The ladder for safety will be at a height of approximately 22.6 feet