Question

question
one of the legs of a right triangle measures 3 cm and the other leg measures 18 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 is \(a^{2}+b^{2}=c^{2}\). Here, \(a = 3\) cm and \(b=18\) cm.

Step2: Substitute values into the formula

Substitute \(a = 3\) and \(b = 18\) into \(a^{2}+b^{2}=c^{2}\), we get \(3^{2}+18^{2}=c^{2}\). Calculate \(3^{2}=9\) and \(18^{2}=324\). Then \(9 + 324=c^{2}\), so \(c^{2}=333\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{333}\). Calculate \(\sqrt{333}\approx18.2\) (rounded to the nearest tenth).

Answer:

The measure of the hypotenuse is approximately \(18.2\) cm.