Answer:
The solution in the attached figure
[tex]sin(A)=\frac{12}{13}[/tex]
[tex]sin(B)=\frac{5}{13}[/tex]
[tex]cos(A)=\frac{5}{13}[/tex]
[tex]cos(B)=\frac{12}{13}[/tex]
[tex]sin(A)=cos(B)[/tex]
[tex]sin(B)=cos(A)[/tex]
Step-by-step explanation:
we know that
In the right triangle ABC
sin(A)=cos(B) and cos(A)=sin(B)
because
[tex]A+B=90\°[/tex] -------> by complementary angles
step 1
Find sin(A)
The function sine of angle A is equal to divide the opposite side angle A by the hypotenuse
[tex]sin(A)=\frac{BC}{AB}[/tex]
substitute the values
[tex]sin(A)=\frac{12}{13}[/tex]
step 2
Find sin(B)
The function sine of angle B is equal to divide the opposite side angle B by the hypotenuse
[tex]sin(B)=\frac{AC}{AB}[/tex]
substitute the values
[tex]sin(B)=\frac{5}{13}[/tex]
step 3
Find cos(A)
The function cosine of angle A is equal to divide the adjacent side angle A by the hypotenuse
[tex]cos(A)=\frac{AC}{AB}[/tex]
substitute the values
[tex]cos(A)=\frac{5}{13}[/tex]
[tex]cos(A)=sin(B)[/tex]
step 4
Find cos(B)
The function cosine of angle B is equal to divide the adjacent side angle B by the hypotenuse
[tex]cos(B)=\frac{BC}{AB}[/tex]
substitute the values
[tex]cos(B)=\frac{12}{13}[/tex]
[tex]cos(B)=sin(A)[/tex]
