Answer:
[tex]\boxed {\boxed {\sf cos(G)=\frac{5}{13} }}[/tex]
Step-by-step explanation:
First, recall the trigonometric ratios.
- sin(θ)=opposite/hypotenuse
- cos(θ)= adajcent/hypotenuse
- tan(θ)=opposite/adjacent
The question asks us to find the cosine of G. Therefore, we need the adjacent side and the hypotenuse.
- Adjacent: 5 is the side next to angle G (12 is opposite, but we don't need that for cosine).
- Hypotenuse: 13 is the hypotenuse because it is the largest side and opposite the right angle.
Substitute the values into the ratio.
[tex]cos(G)= \frac{adjacent}{hypotenuse}[/tex]
[tex]cos(G)=\frac{5}{13}[/tex]
This fraction cannot be reduced further, so it is the answer.
The cosine of G is 5/13
