Question

a 13 - 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.

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse of a right - triangle and $a$ and $b$ are the other two sides. Here, the length of the ladder $c = 13$ ft and the distance of the bottom of the ladder from the house $a = 8$ ft. Let the height of the top of the ladder from the ground be $b$. So, $b^{2}=c^{2}-a^{2}$.

Step2: Substitute values

Substitute $c = 13$ and $a = 8$ into the formula $b^{2}=c^{2}-a^{2}$. We get $b^{2}=13^{2}-8^{2}=169 - 64=105$.

Step3: Solve for $b$

Take the square root of both sides: $b=\sqrt{105}\approx10.2$ ft.

Answer:

$10.2$ ft