Question

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)

Answer 1

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.

Answer 2

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.