Posted by **may** on Sunday, January 9, 2011 at 9:17am.

Two sides of a triangle are 5 and 8 units respectively. If the included angle is changing at rate of one radian, at what rate is the third side changing when the included angle is 60 degrees?

- Trigonometry -
**drwls**, Sunday, January 9, 2011 at 9:34am
One radian is not a rate. It is an angle. Look at the problem statement again.

- Trigonometry -
**Reiny**, Sunday, January 9, 2011 at 10:05am
drwls is right, you must have left out the units of time.

(e.g. ... is changing at a rate of one radian per minute )

In that case, use the cosine law equation as your starting point

let the third side be x and the angle be Ø

x^2 = 5^2 + 8^2 - 2(5)(8)cosØ

2x dx/dt = 0 + 0 + 80 sinØ dØ/dt

from the original equation, find x , then sub in the given values

pretty easy after that.

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