# Math Help - Related rates question!!!

1. ## Related rates question!!!

Two sides of a triangle have lengths 12 m and 14 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°?

in this question i think i need to use the cosines law right..but how can i take the derivatives of the cosines law??

2. cosine law
$a^2 = b^2 + c^2 - 2bc \cos x$

x is angle between b and c

$2a da/dt = 2bc \sin x dx/dt$
$da/dt = (bc \sin x dx/dt)/a$
$= (bc \sin x dx/dt)/ \sqrt ( b^2 + c^2 - 2bc \cos x)$

now substitute the value of b, c dx/dt and x (we have to find da/dt when x = 60 degree)