Question

find \\(\cos(\beta)\\) in the triangle (right - angled at \\(c\\), with \\(bc = 5\\), \\(ac = 12\\), \\(ab = 13\\)). choose 1 answer: \\(\boldsymbol{a}\\) \\(\frac{5}{12}\\), \\(\boldsymbol{b}\\) \\(\frac{12}{13}\\), \\(\boldsymbol{c}\\) \\(\frac{12}{5}\\), \\(\boldsymbol{d}\\) \\(\frac{5}{13}\\)

Explanation:

Step1: Recall cosine definition

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

Step2: Identify sides for $\beta$

For angle $\beta$, adjacent side is $5$, hypotenuse is $13$ (since hypotenuse is opposite right angle, length $13$).

Step3: Calculate $\cos(\beta)$

$\cos(\beta) = \frac{5}{13}$.

Answer:

D. $\frac{5}{13}$