Question

start by substituting the value of a in the pythagorean theorem equation. the pythagorean theorem says that if a, b, and c are the sides of a right - triangle, where c is the hypotenuse, then: $a^{2}+b^{2}=c^{2}$. $c =?$ $a = 5$ $a^{2}+b^{2}=c^{2}$ $b = 6$

Explanation:

Step1: Substitute value of a

Substitute $a = 5$ into $a^{2}+b^{2}=c^{2}$. So we get $5^{2}+b^{2}=c^{2}$. Since $b = 6$, the equation becomes $5^{2}+6^{2}=c^{2}$.
$5^{2}+6^{2}=c^{2}$

Step2: Calculate squares

Calculate $5^{2}=25$ and $6^{2}=36$. Then the left - hand side of the equation is $25 + 36$.
$25+36=c^{2}$
$61=c^{2}$

Step3: Solve for c

Take the square root of both sides. Since $c$ represents the length of a side of a triangle, we take the positive square root.
$c=\sqrt{61}$

Answer:

$c = \sqrt{61}$