Question

one of the legs of a right triangle measures 2 cm and the other leg measures 7 cm. find the measure of the hypotenuse. if necessary, round to the nearest tenth.

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, the Pythagorean theorem is \(a^2 + b^2 = c^2\), where \(a\) and \(b\) are the legs, and \(c\) is the hypotenuse. Here, \(a = 2\) cm and \(b = 7\) cm.

Step2: Substitute values into the formula

Substitute \(a = 2\) and \(b = 7\) into \(a^2 + b^2 = c^2\):
\(2^2 + 7^2 = c^2\)
\(4 + 49 = c^2\)
\(53 = c^2\)

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{53}\)
Calculate \(\sqrt{53}\approx7.3\) (rounded to the nearest tenth)

Answer:

The measure of the hypotenuse is approximately \(7.3\) cm.