Find Value of Sin C

**magentarita** · May 5th 2009, 09:19 PM

In triangle ABC, sin (A + B) = 3/5.
What is the value of sin C?

**Prove It** · May 5th 2009, 09:41 PM

Originally Posted by magentarita

In triangle ABC, sin (A + B) = 3/5.
What is the value of sin C?

In triangle $ABC, C = 180^\circ - (A + B)^\circ$

So use the formula

$\sin{C} = \sin{[180^\circ - (A + B)^\circ]} = \sin{180^\circ}\cos{(A + B)^\circ} - \cos{180^\circ}\sin{(A + B)^\circ}$

and solve for $\sin{C}$ .

**magentarita** · May 6th 2009, 05:24 AM

Originally Posted by Prove It

In triangle $ABC, C = 180^\circ - (A + B)^\circ$

So use the formula

$\sin{C} = \sin{[180^\circ - (A + B)^\circ]} = \sin{180^\circ}\cos{(A + B)^\circ} - \cos{180^\circ}\sin{(A + B)^\circ}$

and solve for $\sin{C}$ .

I can plug and chug but what are the values of A and B? How do I find the values of A and B. Do I need the values of A and B?

**Prove It** · May 6th 2009, 02:48 PM

You don't need them.

What does $\sin{180^\circ}$ equal?

Once you've found that, what does $\sin{180^\circ}\cos{(A + B)^\circ}$ equal?

What does $\cos{180^\circ}$ equal?

Since you're GIVEN the value of $\sin{(A + B)^\circ}$ , what is $\cos{180^\circ}\sin{(A + B)^\circ}$ ?

**magentarita** · May 6th 2009, 06:18 PM

Originally Posted by Prove It

You don't need them.

What does $\sin{180^\circ}$ equal?

Once you've found that, what does $\sin{180^\circ}\cos{(A + B)^\circ}$ equal?

What does $\cos{180^\circ}$ equal?

Since you're GIVEN the value of $\sin{(A + B)^\circ}$ , what is $\cos{180^\circ}\sin{(A + B)^\circ}$ ?

I now understand what you mean.

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