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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?

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  1. ganeshie8
    • one year ago
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    remember cosine law ?

  2. anonymous
    • one year ago
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    yes

  3. anonymous
    • one year ago
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    i already use it

  4. anonymous
    • one year ago
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    i got x=7

  5. ganeshie8
    • one year ago
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    |dw:1433221845172:dw|

  6. anonymous
    • one year ago
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    we have the same drawing

  7. anonymous
    • one year ago
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    but my answer is x=7

  8. ganeshie8
    • one year ago
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    say \(x\) = length of third side |dw:1433221936411:dw|

  9. anonymous
    • one year ago
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    the answer should be 4.9 units here in my answer key. i dont know how to derive

  10. ganeshie8
    • one year ago
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    \[x^2 ~~=~~ 5^2 + 8^2 - 2*5*8\cos(\theta)\] differentiate both sides implicitly with respect to \(t\), what do you get ?

  11. anonymous
    • one year ago
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    2x dx/dt= 80 sin(theta) dtheta/dx

  12. ganeshie8
    • one year ago
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    do you mean \[2x\frac{dx}{dt} = 80\sin(\theta) \frac{d\theta}{dt}\] ?

  13. anonymous
    • one year ago
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    yes

  14. ganeshie8
    • one year ago
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    plugin the given values

  15. anonymous
    • one year ago
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    is that correct?

  16. ganeshie8
    • one year ago
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    Yes, plugin \(\frac{d\theta}{dt} = 1\) , \(\theta = 60\) and \(x=7\)

  17. anonymous
    • one year ago
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    ok wait i will solve.

  18. anonymous
    • one year ago
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    wow

  19. anonymous
    • one year ago
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    i get the answer already

  20. ganeshie8
    • one year ago
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    good

  21. anonymous
    • one year ago
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    80sin60/14 =4.95 units

  22. anonymous
    • one year ago
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    thanks a lot for the big help

  23. ganeshie8
    • one year ago
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    yw!

  24. anonymous
    • one year ago
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    wow ur an engineer

  25. anonymous
    • one year ago
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    i am also an engineering student

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