Answer:
[tex]\sf \sin A=\boxed{\dfrac{5}{13}}\quad\cos A=\boxed{\dfrac{12}{13}}\quad\tan A=\boxed{\dfrac{5}{12}}[/tex]
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
- [tex]\theta[/tex] is the angle
- O is the side opposite the angle
- A is the side adjacent the angle
- H is the hypotenuse
Given:
- [tex]\theta[/tex] = A
- O = BC = 5
- A = AC = 12
- H = AB = 13
[tex]\implies \sf \sin A=\dfrac{5}{13}\quad\cos A=\dfrac{12}{13}\quad\tan A=\dfrac{5}{12}[/tex]
