Two sides of a triangle have lengths 12 m and 18 m. the angle between them is increasing at a rate of 2°/min. how fast is the length of the third side increasing when the angle between the sides of fixed length is 60°

This is the concept of trigonometry, to solve for the value of the other length will be given cosine rule;

c^2=a^2+b^2-2ab cos C

substituting the values in our formula we get:

c^2=12^2+18^2-2*12*18*cos 60

c^2=144+324-432 cos60

c^2=252

hence

c=sqrt252

c=15.88m

thus the fixed length will be 15.88 m