Question

one of the legs of a right triangle measures 7 cm and the other leg measures 6 cm. find the measure of the hypotenuse. if necessary, round to the nearest tenth.

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 7\) and \(b = 6\), and \(c\) is the hypotenuse.
Substitute the values: \(7^{2}+6^{2}=c^{2}\).

Step2: Calculate \(7^{2}\) and \(6^{2}\)

\(7^{2}=49\) and \(6^{2}=36\).
So, \(49 + 36=c^{2}\), which simplifies to \(85=c^{2}\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{85}\).
Using a calculator, \(\sqrt{85}\approx9.2\).

Answer:

\(9.2\)