Question

find the value of each trigonometric ratio. express answers as simplified fractions.

1. \\(\cos c\\)

\\(\triangle abc\\) is a right triangle with right angle at \\(b\\), \\(ac = 39\\), \\(ab = 36\\), \\(bc = 15\\)

Explanation:

Step1: Recall cosine definition for angle C

For right triangle $\triangle ABC$ (right-angled at $B$), $\cos C = \frac{\text{adjacent side to } C}{\text{hypotenuse}}$

Step2: Identify relevant side lengths

Adjacent side to $C$ is $BC = 15$, hypotenuse $AC = 39$

Step3: Simplify the fraction

$\cos C = \frac{15}{39} = \frac{15\div3}{39\div3} = \frac{5}{13}$

Answer:

$\frac{5}{13}$