A ladder leans against the side of a house. The top of the ladder is 20ft from the ground. The bottom of the ladder is 15 ft from the side of the house. Find the length of the ladder. If necessary, round your answer to the nearest tenth.

Answer 1

We can solve this problem using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let x be the length of the ladder. The ladder, the ground, and the side of the house form a right triangle. The top of the ladder, the bottom of the ladder, and the length of the ladder form a right triangle. Therefore, we have a right triangle with sides of length 20 ft, 15 ft, and x ft.

By the Pythagorean theorem, we have:

(15)^2 + x^2 = (20)^2
225 + x^2 = 400
x^2 = 400 - 225
x^2 = 175
x = sqrt(175)
x ≈ 13.2 ft

Therefore, the length of the ladder is approximately 13.2 ft.