Question

1. in a right triangle with a hypotenuse of 13 units and one leg of 12 units, what is the length of the other leg?

a. 5 units
b. 6 units
c. 10 units
d. 3 units

Explanation:

Step1: Apply Pythagorean theorem

$$a^{2}+b^{2}=c^{2}$$
Let \(c = 13\) (hypotenuse) and \(a = 12\) (one leg). We need to find \(b\).

Step2: Rearrange formula

$$b^{2}=c^{2}-a^{2}$$

Step3: Substitute values

$$b^{2}=13^{2}-12^{2}$$
$$b^{2}=169 - 144$$
$$b^{2}=25$$

Step4: Solve for \(b\)

$$b=\sqrt{25}=5$$

Answer:

A. 5 units