Question 1127033
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The length of the third side, c, is related to the angle x by the law of cosines:<br>
{{{c^2 = 13^2+19^2-2(13)(19)cos(x)}}}
{{{c = sqrt(530-494cos(x))}}}<br>
Find the derivative:<br>
{{{dc/dt = ((1/2)(494sin(x))/sqrt(530-494cos(x)))(dx/dt)}}}<br>
Evaluate the derivative for x = 60 degrees and dx/dt = pi/90 (2 degrees per minute, in radian measure):<br>
{{{dc/dt = ((1/2)(494sin(60))/sqrt(530-494cos(60)))(pi/90)}}}<br>
This evaluates to 0.444 ft/min, to 3 decimal places.