. The bottom of a 24-ft ladder is 6 ft from the side of a house. Find the distance from the top of the ladder to the ground. Round to the nearest tenth.
19.2 ft
24.7 ft
22.2 ft
23.2 ft
a^2 + b^2 = c^2
6^2 + b^2 = 24^2
36 + b^2 = 576
b^2 = 540
b = 23.24 ft.
To find the distance from the top of the ladder to the ground, we can use the Pythagorean Theorem. The Pythagorean Theorem 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.
In this problem, the ladder forms the hypotenuse of the right triangle, and the distance from the house to the bottom of the ladder forms one of the legs. Therefore, we can set up the equation as follows:
c^2 = a^2 + b^2
Where:
c = length of the ladder
a = distance from the house to the bottom of the ladder
b = distance from the top of the ladder to the ground
Given:
c = 24 ft
a = 6 ft
Substituting the values into the equation, we get:
24^2 = 6^2 + b^2
576 = 36 + b^2
b^2 = 576 - 36
b^2 = 540
To find b, we need to take the square root of both sides:
b = sqrt(540)
b ≈ 23.2 ft (rounded to the nearest tenth)
Therefore, the distance from the top of the ladder to the ground is approximately 23.2 ft.