## anonymous 4 years ago Please help! One side of a triangle is increasing at a rate of 3 cm/s and a second side is decreasing at a rate of 2 cm/s. If the area of the triangle remains constant, at what rate does the angle between the sides change when the first side is 20 cm long, the second side is 30 cm, and the angle is pi/6?

1. experimentX

perhaps the Q meant this |dw:1350751784378:dw|

2. anonymous

I thought this was related rates, but I'm in calc 3, and we are doing differentials and tangent approximations, so I'm kinda lost here. Plus, I don't really remember related rates too well

3. experimentX

|dw:1350751819497:dw| yeah this is related rate.

4. experimentX

|dw:1350751925717:dw|

5. experimentX

Given that $${x = 20} , {dx \over dt} = 3$$ $${y = 30} , {dy \over dt} = -2$$ $A = {1 \over 2} xy \; \sin \theta \\ {dA \over dt} = 0, \\ \text{Find } {d \theta \over dt }$

6. experimentX

If i interpreted the problem correctly ...

7. anonymous

How did you get z=16.14?

8. experimentX

forget that ... it's not necessary.

9. anonymous

It's been along time since I've done related rates, so I may be wrong, but would I take the derivative of dA/dt first?

10. experimentX

also given that $$\theta = {\pi \over 6}$$ differentiate the above ... put the values and get the rest.

11. experimentX

Given area is constant ... dA/dt = 0

12. anonymous

Would I differentiate A=.5 xysin(theta) ? What would I take the derivative with respect to?

13. experimentX

time ... t, also you are given the values of dx/dt and dy/dt

14. anonymous

dA/dt=.5 (dx/dt)ysin(theta)+x(dy/dt)sin(theta)+xy(theta)(cos(theta))(dtheta/dt) ?

15. experimentX

yes ... put the values dA/dt = 0, all values are given, you only need to find the value of d(theta)/dt

16. anonymous

Got it! Thanks!