SOLUTION: The lengths of the diagonals of the rhombus are a and a times root 3. What are the measures of the angles of this rhombus?

Question 1127913: The lengths of the diagonals of the rhombus are a and a times root 3. What are the measures of the angles of this rhombus?

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

In a rhombus, the diagonals are perpendicular and bisect each other. That divides the rhombus into four congruent right triangles.

In each of the triangles, the legs are half the lengths of the diagonal; in this problem the legs are a/2 and (a*sqrt(3))/2. Since the ratio of the lengths of the legs is 1:sqrt(3), the triangles are 30-60-90 right triangles.

And that makes the angles of the rhombus 60 and 120 degrees.
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