SOLUTION: Two sides of a triangle have lengths 13 m and 19 m. The angle between them is increasing at a rate of 2°/min. How fast is the length of the third side increasing when the angle bet

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Question 1127033: Two sides of a triangle have lengths 13 m and 19 m. The angle between them is increasing at a rate of 2°/min. How fast is the length of the third side increasing when the angle between the sides of fixed length is 60°? (Round your answer to three decimal places.)
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The length of the third side, c, is related to the angle x by the law of cosines:

c%5E2+=+13%5E2%2B19%5E2-2%2813%29%2819%29cos%28x%29
c+=+sqrt%28530-494cos%28x%29%29

Find the derivative:

dc%2Fdt+=+%28%281%2F2%29%28494sin%28x%29%29%2Fsqrt%28530-494cos%28x%29%29%29%28dx%2Fdt%29

Evaluate the derivative for x = 60 degrees and dx/dt = pi/90 (2 degrees per minute, in radian measure):

dc%2Fdt+=+%28%281%2F2%29%28494sin%2860%29%29%2Fsqrt%28530-494cos%2860%29%29%29%28pi%2F90%29

This evaluates to 0.444 ft/min, to 3 decimal places.