Question

find the value of c. use the pythagorean theorem to help you. start by substituting the value of a and b 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: a² + b² = c². b = 2 a = 9 c =?

Explanation:

Step1: Substitute values into formula

Given $a = 9$ and $b = 2$, substitute into $a^{2}+b^{2}=c^{2}$. So we have $9^{2}+2^{2}=c^{2}$.

Step2: Calculate squares

$9^{2}=81$ and $2^{2}=4$, so $81 + 4=c^{2}$, which simplifies to $c^{2}=85$.

Step3: Solve for c

Taking the square - root of both sides, $c=\sqrt{85}$ (we consider the positive value since $c$ represents the length of a side of a triangle).

Answer:

$c = \sqrt{85}$