Question

a ladder leans against the side of a house. the top of the ladder is 12 ft from the ground. the bottom of the ladder is 9 ft from the side of the length of the ladder. if necessary, round your answer to the nearest tenth. ? 12 ft 9

Explanation:

Step1: Identify the triangle type

The ladder, house, and ground form a right triangle. The ladder is the hypotenuse (\(c\)), the height on the house is one leg (\(a = 12\) ft), and the distance from the house is the other leg (\(b = 9\) ft).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). Substitute \(a = 12\) and \(b = 9\):

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Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{225}=15\) (since length can't be negative).

Answer:

15