Question

consider this right triangle with given measures.
what is the length of the missing leg?

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Let \(a = 5\), \(c=\sqrt{61}\), and \(b\) be the missing leg. Then \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(a = 5\) and \(c=\sqrt{61}\) into the formula: \(b^{2}=(\sqrt{61})^{2}-5^{2}\).
Since \((\sqrt{61})^{2}=61\) and \(5^{2}=25\), we have \(b^{2}=61 - 25\).

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

\(b^{2}=61-25=36\).

Step4: Find \(b\)

Take the square root of both sides: \(b=\sqrt{36}\). Since \(b>0\) (length), \(b = 6\).

Answer:

\(6\mathrm{ft}\)