Question

1. if one leg of a right triangle is 5 units and the hypotenuse is 13 units, what is the length of the other leg?

a. 12 units
b. 8 units
c. 15 units
d. 10 units

Explanation:

Step1: Recall Pythagorean theorem

For right triangle: $a^2 + b^2 = c^2$, where $c$ is hypotenuse, $a,b$ are legs.

Step2: Rearrange for unknown leg

Let unknown leg = $x$. $x^2 = c^2 - a^2$

Step3: Substitute given values

$x^2 = 13^2 - 5^2 = 169 - 25 = 144$

Step4: Solve for $x$

$x = \sqrt{144} = 12$

Answer:

a. 12 units