Question

a 12 - ft ladder leans against the side of a house. the bottom of the ladder is 8 ft from the side of the house. how high is the top of the ladder from the ground? if necessary, round your answer to the nearest tenth.
the top of the ladder is 8.9 ft from the ground
the top of the ladder is 9.2 ft from the ground
the top of the ladder is 16.5 ft from the ground
the top of the ladder is 14.4 ft from the ground

Explanation:

Step1: Assume right - triangle situation

The ladder, the ground, and the house form a right - triangle. The length of the ladder is the hypotenuse $c = 12$ ft and the distance from the base of the ladder to the house is $a = 8$ ft. We want to find the height $b$ (the distance from the ground to the top of the ladder).
According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$.

Step2: Rearrange the formula to solve for $b$

We get $b=\sqrt{c^{2}-a^{2}}$.
Substitute $c = 12$ and $a = 8$ into the formula: $b=\sqrt{12^{2}-8^{2}}=\sqrt{144 - 64}=\sqrt{80}\approx8.9$ ft.

Answer:

The top of the ladder is 8.9 ft from the ground.