Help! Is this how to use Law of Sines?

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I have this problem on my math hw... is this how I solve it??

In a triangle where side a is opposite angle A, and side b is opposite angle B and so on....
Given A = 31 degrees, B = 23 degrees and c = 112 feet.

So heres what I think I should do. first i do 180 - (A + B) = 126, so C = 126 degrees. Now 126/112 = 23/x , so side b = 20.44 feet..

Is this how to solve the problem?

One way to check your answer would be to reduce the problem down to a pair of right angled triangles. Then use

sine theta = opposite / hypotenuse
cosine theta = adjacent / hypotenuse

But lets do it with the law of sines

Angle C = 180 - (A+B),

So Angle C = 126 degrees

Now Sine C = 0.80902

Now use the following equation

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

As c is 112 feet,

c / (sine C) = 138.44 feet

Now rearrange the equation

b / (sine B) = c / (sine C)

To b = c (Sine B) / Sine C

Which gives you something very different to the answer you got. I think that you can do the rest yourself, as it is your homework I will not do it for you. My reason for not helping you further right now is that you need to learn, and by doing it yourself you stand a better chance than if I just give you the final answer.

But if you get stuck I think you should consult a maths textbook or one of the maths wizards. You can try PMing me but I can not stay online all day so I might not see your PM until it is too late.

I have just checked the wikipedia article http://en.wikipedia.org/wiki/Right_angl ... and_angles

And it does appear to be correct, I normally do not recomend wikipedia as it is not always correct or well written but the version I just read looks OK and it is correct.

Have fun with your maths.

_________________
Health is a state of physical, mental and social wellbeing and not merely the absence of disease or infirmity I am not a jigsaw, I am a free man !

Diagnosed under the DSM5 rules with autism spectrum disorder, under DSM4 psychologist said would have been AS (299.80) but I suspect that I am somewhere between 299.80 and 299.00 (Autism) under DSM4.

i didnt get what u were doing with the c's, so used a and b. does this look right?

112/sin(126) = x/sin(23) so b=112*sin(23)/sin(126) = 54.09 ft

Thanks

You got the same answer as me, I wish that the WP would allow me to use Greek characters like alpha, beta, gamma and delta as it would have made things a little more clear.

The fact that you agreed with my answer reminds me

"Great minds think alike, but fools seldom beg to differ"

_________________
Health is a state of physical, mental and social wellbeing and not merely the absence of disease or infirmity I am not a jigsaw, I am a free man !

Diagnosed under the DSM5 rules with autism spectrum disorder, under DSM4 psychologist said would have been AS (299.80) but I suspect that I am somewhere between 299.80 and 299.00 (Autism) under DSM4.

lol so i guess i did that one correctly. Thanks alot for your help! I really appreciate it.

So I tried to use the same formula on this problem, but it didn't work? Or maybe I did a step wrong?

Given: b = 5 a = 15 and angle B = 50 degrees.
So I used Law of Sines: Sin A / a = Sin B / b
So Sin A / 15 = Sin 50 / 5 ,
So 5 * Sin A = 15 * Sin 50,
Sin A = (15 * Sin 50) / 5
which equals to 2.2.... which doesnt make sense because that's not a Sine value for a number.

Did I do a step wrong??

Thanks again