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 \(c\), \(c^{2}=a^{2}+b^{2}\). Here \(a = 14\) and \(b = 48\).
\[c^{2}=14^{2}+48^{2}\]

Step2: Calculate squares of the values

\[14^{2}=196\] and \[48^{2}=2304\]. Then \(c^{2}=196 + 2304\).
\[c^{2}=2500\]

Step3: Find the square - root of \(c^{2}\)

\[c=\sqrt{2500}\]
\[c = 50\]

Answer:

50