Respuesta :

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]