SOLUTION: I need help with finding the length of the longer diagonal from AC ABCD IS A PARALLELOGRAM AB = 3.8cm BC = 7.9cm BAD = 48� Height is 2.8cm I'm sure, but if I made a mistake,

Question 1103093: I need help with finding the length of the longer diagonal from AC
ABCD IS A PARALLELOGRAM
AB = 3.8cm BC = 7.9cm BAD = 48�
Height is 2.8cm I'm sure, but if I made a mistake, feel free to correct me. Thanks

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Yes; the height is (approximately) 2.8cm -- as calculated by 3.8*sin(48).

There are ways to find the lengths of the diagonals using the height; but they are very roundabout and inefficient.

Do you know the law of cosines? It makes finding the lengths of the diagonals easy.

In a triangle, the law of cosines relates the length of the third side (c) to the lengths of the other two sides (a and b) and the angle between those other two sides (C):
.

In your problem, each diagonal is the third side of a triangle with legs 3.8cm and 7.9cm. To find the short diagonal, the angle is 48 degrees; to find the long diagonal, the angle is 180-48=132 degrees.

You want the long diagonal, so

Use a calculator.... I get 10.2 (to one decimal place).
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