document.write( "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.) \n" ); document.write( "

Algebra.Com's Answer #743438 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The length of the third side, c, is related to the angle x by the law of cosines:

\n" ); document.write( " $\"c%5E2+=+13%5E2%2B19%5E2-2%2813%29%2819%29cos%28x%29\"$
\n" ); document.write( " $\"c+=+sqrt%28530-494cos%28x%29%29\"$

\n" ); document.write( "Find the derivative:

\n" ); document.write( " $\"dc%2Fdt+=+%28%281%2F2%29%28494sin%28x%29%29%2Fsqrt%28530-494cos%28x%29%29%29%28dx%2Fdt%29\"$

\n" ); document.write( "Evaluate the derivative for x = 60 degrees and dx/dt = pi/90 (2 degrees per minute, in radian measure):

\n" ); document.write( " $\"dc%2Fdt+=+%28%281%2F2%29%28494sin%2860%29%29%2Fsqrt%28530-494cos%2860%29%29%29%28pi%2F90%29\"$

\n" ); document.write( "This evaluates to 0.444 ft/min, to 3 decimal places. \n" ); document.write( "

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