SOLUTION: In a rhombus one side 10 cm and an angle in 37°. Find the area and find the length of a diagonal?

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Question 1102427: In a rhombus one side 10 cm and an angle in 37°. Find the area and find the length of a diagonal?
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Two angles of the rhombus are 37°; the other two are 143°.

The height of the rhombus is 10%2Asin%2837%29+=+6.018

The area of the rhombus is base times height, 10%286.018%29+=+60.18

One way to find the lengths of the diagonals is with the law of cosines.

Long diagonal:
c+=+sqrt%2810%5E2%2B10%5E2-2%2810%29%2810%29cos%28143%29%29+=+18.966
Short diagonal:
c+=+sqrt%2810%5E2%2B10%5E2-2%2810%29%2810%29cos%2837%29%29+=+6.346