Solve the triangle.

A = 46°, a = 34, b = 27

Question

Solve the triangle. 

A = 46°, a = 34, b = 27

anonymous · Answer

B = 34.8°, C = 99.2°, c ≈ 28

campbell_st · Answer

well you can find B using the law of sines 

and then C by angle sum of a triangle 

and c by law of sines or law of cosines

campbell_st · Answer

well c seems a little out... 

if C is the largest angle 99  then c has to be the longest side... 

B seems fine

hero · Answer

@melacho It's best to post only one question at a time.

hero · Answer

Are you here?

hero · Answer

If you want help, you should respond properly. Open Study doesn't work like Yahoo Answers where you just sit and wait for someone to answer your question. We have an expectation for the user to engage in the process of finding the solution to a problem.

anonymous · Answer

UMMM I know how to do this... and i know everyone that helps me knows i hate when people give me the answers

anonymous · Answer

@campbell_st  B = 34.8°, C = 99.2°, c ≈ 46.7

hero · Answer

Did you figure out the first one yet?

anonymous · Answer

i only asked one question dude...

campbell_st · Answer

the answer for c now makes more sense...

anonymous · Answer

thank you c:

hero · Answer

I think there are two solutions for this.

hero · Answer

@melacho

anonymous · Answer

care to explain?

hero · Answer

Yes. Basically, I set up the problem using law of sines as such:

$$\frac{\sin(46)}{34}= \frac{x}{27}$$

$$x \approx 0.57$$

hero · Answer

Of course x = $\sin B$ so

$\sin B = 0.57$

hero · Answer

If you take the inverse sine of both sides you get

$\sin^{-1}(0.57) = 34.7502$

However, you should always perform this operation

180 - 34.7502

hero · Answer

Afterwards you will get 146

Then you should check to make sure $\sin(146)$ isn't also 0.57

hero · Answer

If it is, then that means you have a two triangle case.

hero · Answer

Actually it's more like $\sin(145.2497) \approx 0.57$

hero · Answer

Either way, as you can see, you have a two triangle case, so you have to solve for both.

campbell_st · Answer

but if you use the ambiguous case that can occur in the law of sines... 

given 1 angle is A =  46  how can a 2nd angle be 146  so the 2nd triangle case doesn't exist..

hero · Answer

I knew there was something else I was supposed to check regarding that. It's been a while.