In the triangle shown below, only three sides were given. I have to calculate the three angles. I calculated angle at A as $44.04^o$ using the Cosine rule. Then I decided to calculate the angle at B using the Sine rule.
I wrote: $\frac{\sin 44.04}{3.6}=\frac{\sin B}{3.04}$.
This gives: sin B = 0.5870
But sin B = 0.5870 will give two values for B. They are: $35.95^o$ and $144.05^o$
Which of these two values shall I choose?
I can put aside angle B and try to find angle C. But there also, I will get an acute angle and an obtuse angle. So I am confused as to how to apply the Sine rule in this problem. Please help. Thanks.
2 Answers
$\begingroup$You have to choose $35.95^o$,else the total sum of all interior angles of a triangle would be greater than $180^o$.Also,you can observe that a>b,thus angle A should be greater than angle B.
$\endgroup$ $\begingroup$As $b$ is the smallest side, $B$ is the smallest angle, so it must be the $35.95^\circ$. Similarly, $c$ is the largest side.
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