Question

5 which ratio represents cos a in the accompanying diagram of △abc? 1) \\( \frac { 5 } { 13 } \\) 2) \\( \frac { 12 } { 13 } \\) 3) \\( \frac { 12 } { 5 } \\) 4) \\( \frac { 13 } { 5 } \\)

Explanation:

Step1: Recall the cosine formula

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

Step2: Identify the sides relative to angle \(A\)

For angle \(A\) in right - triangle \(ABC\) (\(\angle C = 90^{\circ}\)), the adjacent side to angle \(A\) is \(AC = 5\), and the hypotenuse is \(AB=13\).

Answer:

1. \(\frac{5}{13}\)