## Wislar Group Title 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? one year ago one year ago

1. experimentX Group Title

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

2. Wislar Group Title

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 Group Title

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

4. experimentX Group Title

|dw:1350751925717:dw|

5. experimentX Group Title

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 Group Title

If i interpreted the problem correctly ...

7. Wislar Group Title

How did you get z=16.14?

8. experimentX Group Title

forget that ... it's not necessary.

9. Wislar Group Title

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 Group Title

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

11. experimentX Group Title

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

12. Wislar Group Title

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

13. experimentX Group Title

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

14. Wislar Group Title

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

15. experimentX Group Title

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

16. Wislar Group Title

Got it! Thanks!