Question

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

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with legs of lengths \(a\) and \(b\) and hypotenuse of length \(c\), \(c^{2}=a^{2}+b^{2}\). Here, \(a = 6\) m and \(b = 8\) m.

Step2: Apply the Pythagorean theorem

Substitute \(a = 6\) and \(b = 8\) into the formula \(c^{2}=a^{2}+b^{2}\). So \(c^{2}=6^{2}+8^{2}=36 + 64=100\).

Step3: 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:

\(10\)