Question

use the pythagorean theorem to find the length of the unknown side of a right triangle, where a and b represent the lengths of the legs and c represents the hypotenuse. a = 14, c = 50; find b. b = (type an exact answer, using radicals as needed.)

Explanation:

Step1: Write Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. We want to find $b$, so we can rewrite it as $b^{2}=c^{2}-a^{2}$.

Step2: Substitute given values

Substitute $a = 14$ and $c = 50$ into the formula $b^{2}=c^{2}-a^{2}$. Then $b^{2}=50^{2}-14^{2}=2500 - 196$.

Step3: Calculate the value of $b^{2}$

$2500-196 = 2304$. So $b^{2}=2304$.

Step4: Solve for $b$

Take the square - root of both sides. Since $b$ represents the length of a side of a triangle, we take the positive square - root. $b=\sqrt{2304}=48$.

Answer:

$48$