Answer:
sin(B) = cos(90 – B)
Explanation:
Which relationship in the triangle must be true? Triangle A B C is shown. Angle A C B is a right angle. The length of side C B is a, the length of side A C is b, and the length of side A B is c.
sin(B) = sin(A)
sin(B) = cos(90 – B)
cos(B) = sin(180 – B)
cos(B) = cos(A)
Assuming the angles are in degrees, the second relation is always true.
By definition of sine,
sin(B) = AC/AB
cos(90-B) = cos (A) = AC/AB
therefore the second relation is true, for arbitrary values of B.