The sine rule has this one downfall.

You need to 180 - your acute answer to obtain the obtuse version. The sine of both angles will have the same value.

So let’s say sin x = 1/2.

Then x can be 30 or 180 - 30.

so basically the acute i’ve got is not on the diagram itself ..?

Either of the two cases will be possible, and will in fact lead to two completely different triangles.

From the shape, however, that angle of interest appears to be obtuse. If it is really an obtuse angle, we would have to reject the acute case. It is the case here, as they requested for an obtuse angle. So we have to reject our acute answer.

oo okay thankyou

The treatment of why two angles are possible is covered in A Maths trigo, where they made mention of the ASTC quadrants. E Maths only takes the result of it and puts the scenario in the AS quadrants (angles 0 to 180).

ahh yes i see..