Question

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

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), the Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\). Here \(a = 4\)m and \(b = 4\)m. So \(c^{2}=4^{2}+4^{2}\).

Step2: Calculate the sum of the squares of the legs

\(4^{2}=16\), so \(4^{2}+4^{2}=16 + 16=32\). Then \(c^{2}=32\).

Step3: Solve for \(c\)

\(c=\sqrt{32}\). Simplifying, \(c = \sqrt{16\times2}=4\sqrt{2}\approx4\times1.414 = 5.7\)m.

Answer:

\(5.7\)