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 height on the house (20 ft), the distance from the house to the bottom of the ladder (15 ft), and the ladder form a right - angled triangle. The ladder is the hypotenuse.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 15\), \(b = 20\), and \(c\) is the length of the ladder. So \(c=\sqrt{a^{2}+b^{2}}=\sqrt{15^{2}+20^{2}}\).

Step3: Calculate the values inside the square - root

First, calculate \(15^{2}=225\) and \(20^{2}=400\). Then \(15^{2}+20^{2}=225 + 400=625\).

Step4: Find the square - root

\(c=\sqrt{625}=25\)

Answer:

25