SOLUTION: A side and a diagonal of a parallelogram are 12 inches and 19 inches respectively. The angle between the diagonals, opposite the given side, is 124 degrees. Find the length of the

Algebra ->  Trigonometry-basics -> SOLUTION: A side and a diagonal of a parallelogram are 12 inches and 19 inches respectively. The angle between the diagonals, opposite the given side, is 124 degrees. Find the length of the       Log On


   

Question 1172080: A side and a diagonal of a parallelogram are 12 inches and 19 inches respectively. The angle between the diagonals, opposite the given side, is 124 degrees. Find the length of the other diagonal.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!



Use the law of cosines:

19%5E2=x%5E2%2B12%5E2-2%2812%29%28x%29cos%28124%5Eo%29

361=x%5E2%2B144-%2824x%29%28-0.5591929035%29

361=x%5E2%2B144%2B13.42062968x

x%5E2%2B144%2B13.42062968x-347.5793703=0

Solve by the quadratic formula:

x=9.476974162

We draw it with the other diagonal:



y%5E2=9.476974162%5E2%2B12%5E2-2%289.476974162%29%2812%29cos%2856%5Eo%29

y%5E2=106.626

y+=+10.326  <--answer (length of other diagonal.)

Edwin