Question

in a right triangle, if a = 5 and c = 13, what is the value of b?
a 9
b 10
c 12
d 11

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$ (assuming $c$ is the hypotenuse). We need to find $b$, so $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute the given values

Given $a = 5$ and $c = 13$. Then $b=\sqrt{13^{2}-5^{2}}=\sqrt{169 - 25}=\sqrt{144}$.

Step3: Calculate the square - root

$\sqrt{144}=12$.

Answer:

C. 12