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:
\(c^2 = a^2 + b^2\)
\(24^2 = 8^2 + b\)
\(576 = 64 + b^2\)
\(b^2 = 576 - 64\)
\(b^2 = 512\)
\(b = \sqrt{512}\)
\(b = 22.627417 \to \boxed{\boxed{b \approx 22.6}}\end{array}}\qquad\quad\checkmark\)
Answer:
The ladder for safety will be at a height of approximately 22.6 feet
