# Given angle A and two sides, find Angle B.

1. Jun 23, 2009

### JacklinH.

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

In triangle ABC, A=65 degrees, b=9, and a=10. Find B.

2. Relevant equations

3. The attempt at a solution

I honestly don't know how to start this problem... I tried to use the law of cosines to find side C, and then again to find Angle B, but that answer was incorrect. I haven't been in Trig for two years, and can't think of how else to start it.

Thanks for any help!

2. Jun 23, 2009

### Bohrok

Try the law of sines.

3. Jun 23, 2009

### Дьявол

First use the sine to find h, and then use again the sine to find B, using arcsin(B).

$$\sin A = \frac{h}{b}\text{ and } \sin B = \frac{h}{a}.$$

Regards.

Last edited: Jun 23, 2009
4. Jun 23, 2009

### HallsofIvy

Staff Emeritus
so that h= b sin A= a sin B and, as a result, $\frac{sin A}{a}= \frac{sin B}{b}$. That is the "sine law" Bohrok is talking about.

Last edited: Jun 23, 2009
5. Jun 23, 2009

### Дьявол

Yes, you're right. I misspelled the words. I thought of "sine" and not "sine law".

Anyway, the things are same, and he would come up with the same result.

6. Jun 23, 2009

### HallsofIvy

Staff Emeritus
Yes, I wasn't criticizing, just pointing out to JacklinH that you were both giving the same advice!