# Solve a Triangle using Trigonometry

1. Apr 14, 2012

### okh

1. The problem statement, all variables and given/known data
http://img23.imageshack.us/img23/9427/imageyakj.jpg [Broken]
AC+CB=24
The bisector = 8.
Find angle DCB, i.e. x.

2. Relevant equations
The Law of sines, I think.

3. The attempt at a solution

Last edited by a moderator: May 5, 2017
2. Apr 14, 2012

### praharmitra

You are right by guessing Law of sines. Why don't you show what work you've done till now and where exactly you're stuck?

3. Apr 14, 2012

### okh

Last edited by a moderator: May 5, 2017
4. Apr 14, 2012

### praharmitra

The first three equations you've written down are correct. The answer is indeed pi/5. Check your calculation again. If you still don't find your mistake, write down your step by step solution, and i'll tell you where you're going wrong.

Last edited by a moderator: May 5, 2017
5. Apr 14, 2012

### okh

I've found my mistake, now I get 3cos^2x-sin^2x-2cosx=0 and the solution is pi/5.
Thank you very much for helping!

6. Apr 14, 2012

### Curious3141

A word of advice, though. It's never a good idea to mix two different angle measures. Since you started in degrees, you should finish in the same. So the answer is x = 36 degrees.

7. Apr 14, 2012

### sharks

I agree, with Curious3141. You might also want to justify why you rejected the other value of x, which is 108 degrees.

I see 2 reasons:
1. Since x is an acute angle from the figure, x cannot be 108 degrees.
2. If you evaluate the angle CAD, using x=108 degrees, you'll get a negative value, which is not possible.

I hope that helped you a little bit.