Question

one of the legs of a right triangle measures 9 cm and the other leg measures 8 cm. find the measure of the hypotenuse. if necessary, round to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 9\) and \(b = 8\), and hypotenuse \(c\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\).
So, \(c^{2}=9^{2}+8^{2}\).

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

\(9^{2}=81\) and \(8^{2}=64\). Then \(c^{2}=81 + 64\).

Step3: Sum the values

\(81+64 = 145\), so \(c^{2}=145\).

Step4: Solve for \(c\)

\(c=\sqrt{145}\approx12.0416\).

Step5: Round to the nearest tenth

Rounding \(12.0416\) to the nearest tenth gives \(c\approx12.0\).

Answer:

\(12.0\) cm