Question

a ladder leans against the side of a house. the top of the ladder is 20 ft from the ground. the bottom of the ladder is 15 ft from the side of the house. find the length of the ladder. if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Identify the right - angled triangle

The situation forms a right - angled triangle with the height on the house (20 ft), the distance from the house (15 ft), and the ladder as the hypotenuse.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $a = 15$ and $b = 20$. So $c=\sqrt{a^{2}+b^{2}}=\sqrt{15^{2}+20^{2}}$.

Step3: Calculate the values

First, calculate $15^{2}=225$ and $20^{2}=400$. Then $15^{2}+20^{2}=225 + 400=625$. So $c=\sqrt{625}=25$.

Answer:

25 ft