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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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?

Calculus1
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remember cosine law ?
yes
i already use it

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Other answers:

i got x=7
|dw:1433221845172:dw|
we have the same drawing
but my answer is x=7
say \(x\) = length of third side |dw:1433221936411:dw|
the answer should be 4.9 units here in my answer key. i dont know how to derive
\[x^2 ~~=~~ 5^2 + 8^2 - 2*5*8\cos(\theta)\] differentiate both sides implicitly with respect to \(t\), what do you get ?
2x dx/dt= 80 sin(theta) dtheta/dx
do you mean \[2x\frac{dx}{dt} = 80\sin(\theta) \frac{d\theta}{dt}\] ?
yes
plugin the given values
is that correct?
Yes, plugin \(\frac{d\theta}{dt} = 1\) , \(\theta = 60\) and \(x=7\)
ok wait i will solve.
wow
i get the answer already
good
80sin60/14 =4.95 units
thanks a lot for the big help
yw!
wow ur an engineer
i am also an engineering student

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