Question

1. find the missing side of the right triangle. side c is the hypotenuse. sides a and b are the legs. leave your answers in simplest radical form.

a = 11 m, c = 15 m.
b =

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^{2}+b^{2}=c^{2}\), we need to solve for \(b\), so rearrange the formula to \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values of \(a\) and \(c\)

Given \(a = 11\space m\) and \(c=15\space m\), substitute into the formula: \(b^{2}=15^{2}-11^{2}\). Calculate \(15^{2}=225\) and \(11^{2} = 121\), so \(b^{2}=225 - 121=104\).

Step3: Simplify the radical

Simplify \(\sqrt{104}\), factor \(104 = 4\times26\), so \(\sqrt{104}=\sqrt{4\times26}=2\sqrt{26}\). Since \(b\) represents the length of a side, we take the positive square root.

Answer:

\(2\sqrt{26}\space m\)