Question

sides a and b represent the two legs of a right - triangle, and c represents the hypotenuse. find the length of the unknown side.
a = 14 in., c = 50 in.
the length of the third side is (square) (simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, we want to find $b$, so $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute given values

Given $a = 14$ and $c = 50$, then $b=\sqrt{50^{2}-14^{2}}=\sqrt{(50 + 14)(50 - 14)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$).

Step3: Calculate the values inside the square root

$(50 + 14)(50 - 14)=64\times36$.

Step4: Find the square root

$b=\sqrt{64\times36}=\sqrt{64}\times\sqrt{36}=8\times6 = 48$.

Answer:

$48$ in.