Answer:
Part A) [tex]sin(A)=\frac{2\sqrt{42}}{23}[/tex]
Part B) [tex]cos(A)=\frac{19}{23}[/tex]
Part C) [tex]tan(A)=\frac{2\sqrt{42}}{19}[/tex]
Step-by-step explanation:
Part A) we know that
In the right triangle ABC of the figure the sine of angle A is equal to divide the opposite side angle A by the hypotenuse
so
[tex]sin(A)=\frac{BC}{AB}[/tex]
substitute the values
[tex]sin(A)=\frac{2\sqrt{42}}{23}[/tex]
Part B) we know that
In the right triangle ABC of the figure the cosine of angle A is equal to divide the adjacent side angle A by the hypotenuse
so
[tex]cos(A)=\frac{AC}{AB}[/tex]
substitute the values
[tex]cos(A)=\frac{19}{23}[/tex]
Part C) we know that
In the right triangle ABC of the figure the tangent of angle A is equal to divide the opposite side angle A by the adjacent side angle A
so
[tex]tan(A)=\frac{BC}{AC}[/tex]
substitute the values
[tex]tan(A)=\frac{2\sqrt{42}}{19}[/tex]
