Two sides of a triangle have lengths 8 m and 13 m. The angle between them is increasing at a rate of 0.08 radians /min. How fast is the length of the third side increasing when the angle between the sides of fixed length is π/3 radians.

Answer 1

pi/3 = 60 degree just so I do not have to use radians on my calculator :)

c^2 = a^2 + b^2 - 2 a b cos C
get initial stuff first
cos 60 = 1/2
sin 60 = .866
c^2 = 64 + 169 - 208 cos 60
c^2 = 233 - 104 = 129
c = 11.4
now do the problem
2 c dc/dt = -208 (-sin 60) dC/dt
so
dc/dt = 208(.866)(.08)/(2*11.4)