# Does anyone understand this answer? proving sin(A-B)

1. Jan 17, 2008

### eeuler

I had no clue how to do this and could only grasp the first basic parts but even then i couldn't get it right and in the end i had to look at the answer, which confused me even more. So i was wondering if anyone else understands this, and if so could you describe it in words please?

1. The problem statement, all variables and given/known data

2. Relevant equations
As above

3. The attempt at a solution

I understand the first part, getting cos B from the graph...yet when it gets to the other part '...angle in the bottom right hand corner of the triangle is PI - A...' i don't understand how they came to that...but i was wondering, the sin (PI/2 - A) seems to be related to a trigonometric identity? If someone could explain it that would be great.

2. Jan 17, 2008

### HallsofIvy

Staff Emeritus
The angle in the bottom right hand corner is NOT $\pi- A$. The two non-right angles in a right triangle must add to $\pi/2$. Since the whole angle in the upper left is A, the angle in the bottom righthand corner is $\pi/2- A$.

3. Jan 17, 2008

### eeuler

Thank you for that, it clears some of the confusion, thanks.