30.54 Which relationship in the triangle must be true?

sin (B) = sin (A)

sin (B) = cos (90 - B)

cos (B) = sin (180 - B)

cos (B) = cos (A)

Answer: Choice 2) sin (B) = cos (90-B)

Explanation:

The rule is that

sin (A) = cos (B)

if and only if A+B = 90.

Solving for A gets A = 90-B

So we end up with

sin (90-B) = cos (B)

which is the same as

cos (B) = sin (90-B)