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 = 7, b = 5; find c. c = (type an exact answer, using radicals as needed.)

Explanation:

Step1: Recall Pythagorean theorem

The Pythagorean theorem for a right - triangle is $a^{2}+b^{2}=c^{2}$, where $a$ and $b$ are the legs and $c$ is the hypotenuse.

Step2: Substitute given values

Substitute $a = 7$ and $b = 5$ into the formula: $7^{2}+5^{2}=c^{2}$. Calculate $7^{2}=49$ and $5^{2}=25$. So, $49 + 25=c^{2}$, which simplifies to $c^{2}=74$.

Step3: Solve for $c$

Take the square root of both sides. Since $c$ represents the length of a side of a triangle and must be positive, $c=\sqrt{74}$.

Answer:

$\sqrt{74}$