# Trigonometry question, help would be appreciated

• May 4th 2010, 12:10 AM
brumby_3
Trigonometry question, help would be appreciated
Find the angles of this ABC triangle where a=120,b=29 and c=101.
I found the angle for c) using the cosine rule where I got 43.60 degrees.
But I can't find A - I tried the sin rule and my answer doesn't match with the answer I've been given. and how to find B?
• May 4th 2010, 02:44 AM
Sine Rule: ambiguous case
Hello brumby_3
Quote:

Originally Posted by brumby_3
Find the angles of this ABC triangle where a=120,b=29 and c=101.
I found the angle for c) using the cosine rule where I got 43.60 degrees.
But I can't find A - I tried the sin rule and my answer doesn't match with the answer I've been given. and how to find B?

When you used the Sine Rule to find $A$, did you get $55.02^o$? If so, you need to remember that there are two possible values of $A$ that both have the same sine: $55.02^o$ and $180 - 55.02 = 124.98^o$.

How do we tell which to choose? The answer is to find the smallest angle of the triangle first (that's the one opposite the shortest side), because you know that one can't possibly be obtuse.

In this case that's $B$, which turns out to be $11.42^o$. Then add $B$ and $C$ together and subtract from $180^o$ to find $A$.