Question

part of a roof truss forms a right triangle with legs that are 5 feet and 8 feet long. how long is the lumber for the hypotenuse of that triangle?
between 6 and 7 feet
13 feet
89 feet
between 9 and 10 feet

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle with legs \(a\) and \(b\), and hypotenuse \(c\), the theorem is \(c = \sqrt{a^{2}+b^{2}}\). Here, \(a = 5\) feet and \(b = 8\) feet.

Step2: Calculate \(a^{2}+b^{2}\)

\(a^{2}=5^{2} = 25\), \(b^{2}=8^{2}=64\). Then \(a^{2}+b^{2}=25 + 64=89\).

Step3: Find the square root of 89

We know that \(9^{2}=81\) and \(10^{2}=100\). Since \(81<89<100\), \(\sqrt{81}<\sqrt{89}<\sqrt{100}\), so \(9<\sqrt{89}<10\). Thus the length of the hypotenuse is between 9 and 10 feet.

Answer:

Between 9 and 10 feet