Question

triangle abc is a right triangle. which equation could be used to determine the length of side ac?
a
x
15
c
8
b
$x = 8^2 + 15^2$
$x = \sqrt{15^2 - 8^2}$
$x = 15^2 - 8^2$
$x = \sqrt{8^2 + 15^2}$

Explanation:

Step1: Identify Pythagorean theorem

For right $\triangle ABC$, $a^2 + b^2 = c^2$, where $c$ is hypotenuse.

Step2: Assign values to variables

Here, $AC = x$, $BC = 8$, $AB = 15$ (hypotenuse). So $x^2 + 8^2 = 15^2$.

Step3: Isolate $x^2$

Rearrange to solve for $x^2$: $x^2 = 15^2 - 8^2$.

Step4: Solve for $x$

Take square root of both sides: $x = \sqrt{15^2 - 8^2}$.

Answer:

$x = \sqrt{15^2 - 8^2}$