How Do You Solve for a Using the Law of Sines?

[MathWA]

Homework Statement

Find a by using The Law of Sines by knowing that c=12, angle A=42^o, angle C=69^o.

Homework Equations

(sin A)/a=(sin B)/b=(sin C)/c

The Attempt at a Solution

I tried putting it in, but all I got was this correct, but useless equation:
6511/7990=383/470
I did it 1 more time, but still it wasn't successful.
Please Help!

 

[rpthomps]

I am not sure how you go the numbers you did in the solution attempt. The sine of the angles will give you numbers less than 1. I get the answer 8.6 for a

 

[MathWA]

Well, I did a lot of factoring with decimals, so I must had got them mixed up.
By the way calculators are allowed.

 

[MathWA]

The answer is actually 9.34, but I need the solution(step-by-step work).

 

[rpthomps]

Show me your work.

 

[MathWA]

I am not sure how you go the numbers you did in the solution attempt. The sine of the angles will give you numbers less than 1. I get the answer 8.6 for a

I recalculated and got 61, instead, but its wrong!

 

[MathWA]

Well, I got c equals to 50.

 

[rpthomps]

Can you write out line by line what you are doing, please?

 

[MathWA]

Can you write out line by line what you are doing, please?

That would take a while, but sure, but not now(I'm very busy)
I can give you the last couple of lines:
(0.94)/a=47/ac
c=50
0.94/a=0.77/50
47=0.77a
a is about 61

 

[rpthomps]

well, firstly if 0.94 is your answer to sin42, that isn't right. I get something closer in radian mode.

 

[MathWA]

Oops, I typed the wrong problem!
c is 12, angle A is 110, and angle C is 50
Sorry about that rpthomps!

 

[rpthomps]

That would take a while, but sure, but not now(I'm very busy)
I can give you the last couple of lines:
(0.94)/a=47/ac
c=50
0.94/a=0.77/50
47=0.77a
a is about 61

So, is this work using the new values then? where did 47 come from?

 

[rpthomps]

$$\frac{a}{sin110}=\frac{12}{sin50}$$

This is how I would start it. THen I would use algebra to solve for the unknown.

 

[MathWA]

I figured the problem out! Thank you, rpthomps!

 

[MathWA]

I made the problem too confusing!

 

[Mark44]

The Attempt at a Solution

I tried putting it in, but all I got was this correct, but useless equation:
6511/7990=383/470

Yes, this is useless. Since you're trying to solve for a, your equation here should have a in it somewhere.

The answer is actually 9.34, but I need the solution(step-by-step work).

That's not how it works here. We'll help you get to a solution, but we aren't going to give it to you step by step.

Start with what rpthomps write in post #13.

 

[rpthomps]

I figured the problem out! Thank you, rpthomps!

You're welcome