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)
Accepted Solution
A:
Answer:sin(B) = cos(90 – B) Step-by-step 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/ABcos(90-B) = cos (A) = AC/ABtherefore the second relation is true, for arbitrary values of B.