Perfect application for the Law of Cosines.
c^2 = a^2 + b^2 - 2ab cos C; here we want C, the angle opposite the 14 m side.
(14 m)^2 = (8 m)^2 + (12 m)^2 - 2(8 m)(12 m) cos C
196 = 64 + 144 - 192 cos C
-12 = -192 cos C, or cos C = 0.0625
Then C = arccos 0.0625 = 1.5083 radians
1.5083 radians 180 deg
= ----------------------- * -------------------
1 3.14159 rad
= 86.417 degrees
= 86 degrees, when rounded off as specified.
