Question

a window washer leans a 13 - foot ladder against a house. the bottom of the ladder is 5 feet from the house. how high is the second - floor window off the ground? 12 feet 8 feet 18 feet $sqrt{194}$

Explanation:

Step1: Identify right - triangle

The ladder, the ground, and the side of the house form a right - triangle. The length of the ladder is the hypotenuse $c = 13$ feet and the distance from the bottom of the ladder to the house is one leg $a = 5$ feet. Let the height of the window from the ground be $b$.

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. We can solve for $b$: $b=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute values

Substitute $a = 5$ and $c = 13$ into the formula: $b=\sqrt{13^{2}-5^{2}}=\sqrt{169 - 25}=\sqrt{144}$.

Step4: Calculate the value of $b$

$\sqrt{144}=12$.

Answer:

12 feet