Question

a right triangle has legs measuring 5 units and b units, with a hypotenuse of 13 units. what is the exact value of b? 6 12 10 \\( \sqrt { 100 } \\)

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(a = 5\), \(c = 13\). So \(5^{2}+b^{2}=13^{2}\).

Step2: Simplify the equation

\(25 + b^{2}=169\). Then \(b^{2}=169 - 25\).

Step3: Calculate \(b^{2}\)

\(b^{2}=144\).

Step4: Solve for \(b\)

Since \(b>0\) (length), \(b=\sqrt{144}=12\).

Answer:

\(12\)