Question

square roots and the pythagorean theorer vectored instruction find the length of “c” using the pythagorean theorem.

Explanation:

Step1: Recall Pythagorean Theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here \(a = 14\) and \(b = 48\).

Step2: Substitute values into the formula

\(c^{2}=14^{2}+48^{2}\). Calculate \(14^{2}=196\) and \(48^{2}=2304\). So \(c^{2}=196 + 2304=2500\).

Step3: Solve for \(c\)

Take the square - root of both sides. Since \(c>0\) (length), \(c=\sqrt{2500}=50\).

Answer:

50