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?

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

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 $\displaystyle B$, which turns out to be $\displaystyle 11.42^o$. Then add $\displaystyle B$ and $\displaystyle C$ together and subtract from $\displaystyle 180^o$ to find $\displaystyle A$.

Grandad