Question

determine \\(\cos(a)\\) and \\(\cos(b)\\).

Explanation:

Step1: Recall cosine definition

In a right triangle, $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$.

Step2: Find $\cos(A)$

For $\angle A$, adjacent side is $AC = 16$, hypotenuse is $AB = 20$. So $\cos(A) = \frac{16}{20} = \frac{4}{5}$.

Step3: Find $\cos(B)$

For $\angle B$, adjacent side is $BC = 12$, hypotenuse is $AB = 20$. So $\cos(B) = \frac{12}{20} = \frac{3}{5}$.

Answer:

$\cos(A) = \frac{4}{5}$, $\cos(B) = \frac{3}{5}$