Question

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

Explanation:

Step1: Apply 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. Here, \(a = 6\space m\) and \(b=8\space m\). So we substitute these values into the formula: \(6^{2}+8^{2}=c^{2}\)

Step2: Calculate the squares

Calculate \(6^{2}=36\) and \(8^{2} = 64\). Then \(36 + 64=c^{2}\)

Step3: Sum the values

\(36+64 = 100\), so \(c^{2}=100\)

Step4: Solve for c

Take the square root of both sides. Since \(c\) represents the length of a side of a triangle, we take the positive square root. So \(c=\sqrt{100}=10\)

Answer:

\(10\)