Thread: Trigonometry question, help would be appreciated

1. 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?

2. Sine Rule: ambiguous case

Hello brumby_3
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