maths trigonometry ambiguous sine rule help

I have completed these questions but I cannot access the answers, can someone who is good at maths check if its correct please:

state in each case if there is one or two possible solutions

In triangle LMN n=7.3, l=5.1 and angle L =41.1
my answer was two solutions, either 69 degrees or 28.9 degrees.

the 2nd question is triangle ABC, b=3.19, a=3.8 and angle A=72 degrees.
my answer is just one solution= 53 degrees

Any help greatly appreciated.

could you perhaps send a picture or screenshot of the question? When you label a side it should be 2 letters

Hopefully you can view this, thanks for the reply

Hopefully you can view this, thanks for the reply

Could you also perhaps attach your working out as I have an answer but it is different to yours

For a) the multiple values occur with one <90 and the other >90? A sketch usually helps.
https://www.mathsisfun.com/algebra/trig-sine-law.html

I’ll attach what I did in a second, although it’ll be super messy and probably wrong


Sorry I don’t really get it, so it has to be bigger than 90?

I’ll attach what I did in a second, although it’ll be super messy and probably wrong


Sorry I don’t really get it, so it has to be bigger than 90?

For b) assuming the numbers are right, what would the obtuse solution be? Why can it be neglected? Tbh. The initial sketch is important. Your 72 angle is far too small.

I agree with your answer there although I would give my answer to 1 d.p.

you understand why you do the step with 180 - angle = other possible angle right?

so the obtuse angle would be 180- 53= 127 degrees. However 127 + 72 > 180 therefore it cannot be that?

Correct. Assume there are two solutions corresponding to the two values given by asin(). Then rule out as necessary. Check with a sensible sketch.

Another thing is you can write the rule as
sin(A)/a = sin(B)/b = sin(C)/c
If you're calculating angles, there is less to do at the start (fewer errors). Have a good read of that webpage (or your textbook).