Question

question
one of the legs of a right triangle measures 16 cm and the other leg measures 9 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 \(c\), the Pythagorean theorem states \(c = \sqrt{a^2 + b^2}\). Here, \(a = 16\) cm and \(b = 9\) cm.

Step2: Substitute values into formula

Substitute \(a = 16\) and \(b = 9\) into the formula: \(c=\sqrt{16^{2}+9^{2}}\). First, calculate \(16^{2}=256\) and \(9^{2}=81\). Then, \(16^{2}+9^{2}=256 + 81=337\). So, \(c=\sqrt{337}\).

Step3: Calculate and round

Calculate \(\sqrt{337}\approx18.3575\). Rounding to the nearest tenth gives \(18.4\).

Answer:

The measure of the hypotenuse is approximately \(18.4\) cm.