Question

1. in right triangle abc, angle c is a right angle, ab is 25 units long, and bc is 24 units long. what is the length of ac?

a. 1
b. 2
c. 7
d. 49

Explanation:

Step1: Apply Pythagorean theorem

For right triangle $ABC$ with right angle at $C$, the theorem states $AB^2 = AC^2 + BC^2$. Rearrange to solve for $AC$:
$AC^2 = AB^2 - BC^2$

Step2: Substitute given values

$AB=25$, $BC=24$, so:
$AC^2 = 25^2 - 24^2 = 625 - 576 = 49$

Step3: Calculate square root of result

$AC = \sqrt{49} = 7$

Answer:

c. 7