Question

find the value of c. pythagorean theorem: a² + b² = c²

Explanation:

Step1: Identify the values of a and b

Let \(a = 3\)m and \(b=7\)m.

Step2: Apply the Pythagorean theorem

According to \(a^{2}+b^{2}=c^{2}\), we substitute \(a = 3\) and \(b = 7\) into the formula: \(c^{2}=3^{2}+7^{2}=9 + 49=58\).

Step3: Solve for c

Take the square - root of both sides. Since \(c>0\) (as it represents the length of a side of a triangle), \(c=\sqrt{58}\text{ m}\).

Answer:

\(c = \sqrt{58}\text{ m}\)