Question

one of the legs of a right triangle measures 5 cm and the other leg measures 11 cm. find the measure of the hypotenuse. if necessary, round to the nearest tenth.

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Here \(a = 5\) cm and \(b=11\) cm.
So \(c^{2}=5^{2}+11^{2}\).

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

\(5^{2}=25\) and \(11^{2}=121\). Then \(c^{2}=25 + 121=146\).

Step3: Find \(c\)

\(c=\sqrt{146}\approx12.1\) (rounded to the nearest tenth).

Answer:

\(12.1\) cm