Question

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°

Answer 1

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