Ben K. answered • 10/26/16

JHU Grad specializing in Math and Science

Tutor

This is a very interesting problem! Can you recall any relation between two sides of a triangle and the angle between them?

You should remmber the Law of Cosines, which is:

c

^{2}= a^{2}+ b^{2}- 2ab cos(θ)Does that look familiar?

Here, c is the longest side, and a and b are the shorter sides. Theta is the angle between them.

Use implicit differentiation to get...

2c (dc/dt) = -2ab(-sin(θ)) dθ/dt

You want to solve for (dc/dt) now. Remember to convert your angles from degrees to radians. 60 degrees is π/3. 2 degrees/min converts to 2*π/180 = π/90

2c *dc/dt = 2*(11)(18)*sin(π/6)*π/90

= 2(11)(18)(√3/2)(π/90)

= 11*18*√3*π/90

Find 'c' using the original law of cosines, then solve for dc/dt. I will leave the final steps for you to figure out.

I hope this helps!