Question

what is the length of the hypotenuse? if necessary, round to the nearest tenth.
c = \boxed{} meters

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, the Pythagorean theorem is given by \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the lengths of the legs of the right - triangle and \(c\) is the length of the hypotenuse. In this triangle, \(a = 2\) m and \(b=7\) m.

Step2: Substitute values into the formula

Substitute \(a = 2\) and \(b = 7\) into the formula \(a^{2}+b^{2}=c^{2}\). We get \(2^{2}+7^{2}=c^{2}\). Calculate \(2^{2}=4\) and \(7^{2}=49\). Then \(4 + 49=c^{2}\), so \(c^{2}=53\).

Step3: Solve for \(c\)

Take the square root of both sides to find \(c\). \(c=\sqrt{53}\). Calculate \(\sqrt{53}\approx7.3\) (since \(7.3^{2}=53.29\) and \(7.2^{2}=51.84\), and \(53\) is closer to \(53.29\)).

Answer:

\(7.3\)