Two sides of a parallelogram are 30 and 20. One diagonal has a length of 40. What is the length of the other diagonal?
+23245 Labeling the parallelogram in this fashion. AB = 30 BC = 20 CD = 30 DA = 20 AC = 40.
One way to solve this problem is to use the Law of Cosines in this fashion:
1) Find the size of angle(CAB) by using the Law of Cosines on triangle(CAB).
2) Find the size of angle(DAC) by using the Law of Cosines on triangle(DAC).
3) Add the results of steps 1) and 2) to find the size of angle(DAB).
4) Find the length of side BD by using the Law of Cosines on triangle(DAB).
