Question

what is the length of the unknown leg in the right triangle?

√65 ft
√57 ft
9 ft
3 ft

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse (\(c = \sqrt{73}\) ft) and \(b = 8\) ft. Let the unknown leg be \(a\). Then \(a^{2}=c^{2}-b^{2}\).
Substitute \(c=\sqrt{73}\) and \(b = 8\) into the formula: \(a^{2}=(\sqrt{73})^{2}-8^{2}\).

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

Using the property \((\sqrt{x})^{2}=x\) (\(x\geq0\)), \((\sqrt{73})^{2}=73\) and \(8^{2}=64\). So \(a^{2}=73 - 64\).
\(a^{2}=9\).

Step3: Solve for \(a\)

Take the square root of both sides. Since \(a>0\) (length of a side of a triangle), \(a=\sqrt{9}\).
\(a = 3\) ft.

Answer:

\(3\) ft