Question

Nicholas places his 30-foot ladder against a house he is painting.  If the foot of the ladder is 8 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?(1 point) Responses 22.0 ft. 22.0 ft. 31.0 ft. 31.0 ft. 28.9 ft. 28.9 ft. 27.8 ft.

Answer 1

Using the Pythagorean theorem, the ladder reaches a height of approximately 28.9 feet on the house when the foot of the ladder is 8 feet from the base of the house. Therefore correct option is C

Step-by-step explanation:

The question asks how high the ladder reaches on the house if it is a 30-foot ladder and the foot of the ladder is 8 feet away from the house.

We can solve this problem using the Pythagorean theorem which states in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c2 = a2 + b2.

The ladder represents the hypotenuse (c), and the distance from the house represents one side (a). We are solving for the height the ladder reaches on the house, which is the other side (b).

We can set up the equation as follows: 302 = 82 + b2 or 900 = 64 + b2.

Subtracting 64 from both sides gives us b2 = 836.

Taking the square root of both sides, we find b = √836, which is approximately 28.9 feet to the nearest tenth of a foot. So, the ladder reaches 28.9 feet up the house.