## anonymous one year ago pls help me in this problem. 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?

1. ganeshie8

remember cosine law ?

2. anonymous

yes

3. anonymous

4. anonymous

i got x=7

5. ganeshie8

|dw:1433221845172:dw|

6. anonymous

we have the same drawing

7. anonymous

8. ganeshie8

say $$x$$ = length of third side |dw:1433221936411:dw|

9. anonymous

the answer should be 4.9 units here in my answer key. i dont know how to derive

10. ganeshie8

$x^2 ~~=~~ 5^2 + 8^2 - 2*5*8\cos(\theta)$ differentiate both sides implicitly with respect to $$t$$, what do you get ?

11. anonymous

2x dx/dt= 80 sin(theta) dtheta/dx

12. ganeshie8

do you mean $2x\frac{dx}{dt} = 80\sin(\theta) \frac{d\theta}{dt}$ ?

13. anonymous

yes

14. ganeshie8

plugin the given values

15. anonymous

is that correct?

16. ganeshie8

Yes, plugin $$\frac{d\theta}{dt} = 1$$ , $$\theta = 60$$ and $$x=7$$

17. anonymous

ok wait i will solve.

18. anonymous

wow

19. anonymous

20. ganeshie8

good

21. anonymous

80sin60/14 =4.95 units

22. anonymous

thanks a lot for the big help

23. ganeshie8

yw!

24. anonymous

wow ur an engineer

25. anonymous

i am also an engineering student