Question

one of the legs of a right triangle measures 7 cm and the other leg measures 15 cm. find the measure of the hypotenuse. if necessary, round to the nearest tenth.

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem for a right - triangle is \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs and \(c\) is the hypotenuse. Here \(a = 7\) and \(b=15\).
So, \(7^{2}+15^{2}=c^{2}\).

Step2: Calculate the squares

\(7^{2}=49\) and \(15^{2}=225\). Then \(49 + 225=c^{2}\), which gives \(c^{2}=274\).

Step3: Find the value of \(c\)

Take the square root of both sides: \(c=\sqrt{274}\). Using a calculator, \(\sqrt{274}\approx16.6\)

Answer:

\(16.6\)