Question

the lengths of two sides of a right triangle are 5 inches and 8 inches. what is the difference between the two possible lengths of the third side of the triangle? round your answer to the nearest tenth. 2.4 inches 10.0 inches 15.7 inches 3.2 inches

Explanation:

Step1: Find the third side when both are legs

Using the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(a = 5\) and \(b=8\).
\(c=\sqrt{5^{2}+8^{2}}=\sqrt{25 + 64}=\sqrt{89}\approx9.4\)

Step2: Find the third side when one is a leg and the other is the hypotenuse

Let the hypotenuse \(c = 8\), and the leg \(a = 5\). Using \(b=\sqrt{c^{2}-a^{2}}\)
\(b=\sqrt{8^{2}-5^{2}}=\sqrt{64 - 25}=\sqrt{39}\approx6.2\)

Step3: Calculate the difference

\(9.4-6.2 = 3.2\)

Answer:

\(3.2\) inches