In triangle lmn, lm=6,mn=9, and ln=7. find m angle m to the nearest tenth of a degree

To solve for the measure of angle m, use the cosine law formula.

c^2 = a^2 + b^2 - 2ab cos(C)
in the given situation

( LN )^2 = ( LM )^2 + ( MN)^2 - 2(LM)(MN)cos(m)
substitute the given values

7^2 = 6^2 + 9^2 - 2(6)(9)cos(m)
-68 = 2(6)(9)cos(m)
cos(m) = -0.6296
m = arcos ( -0.6296)
m = 129.0 degrees