Question 1062623
Points L, M, N

MN = 27.0
LN = 31.4
Find LM length.


Your composition field shows this but here, making a small change wording :
---------------------------------------------------------------------
In triangle LMN, L = 27.0 cm, m = 31.4 cm, and angle measure at N = 82°. 
Determine the measure of n to the nearest tenth of a centimetre.
-----------------------------------------------------------------------
That means the interior angle between segments MN and LN  is 82 degrees.



The question is asking for the length of segment LM.


Use Law Of Cosines.
{{{27^2+31.4^2-2*27*31.4*cos(82)=LM^2}}}

{{{LM=sqrt(27^2+31.4^2-2(27)(31.4)*cos(82))}}}