Lane places his 30-foot ladder against a house he is painting.%C2%A0 If the bottom of the ladder is 7 feet from the base of the house, how high above the ground is the top of the ladder touching the house, to the nearest tenth of a foot
a. 30ft
b. 20.6ft
c. 29.2ft
d.49ft
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the ladder is the hypotenuse, the distance from the base of the house to the ladder is one side, and the height above the ground is the other side.
Let's call the height above the ground "h". We can set up the equation:
7^2 + h^2 = 30^2
Simplifying, we get:
49 + h^2 = 900
Subtracting 49 from both sides, we get:
h^2 = 851
Taking the square root of both sides, we get:
h = √851 ≈ 29.2
Therefore, the height above the ground that the top of the ladder is touching the house is approximately 29.2 feet.
The answer is c. 29.2ft.