SOLUTION: A rhombus has an 8m side and a 60 degree angle, what is the length of each diagonal?

Question 558113: A rhombus has an 8m side and a 60 degree angle, what is the length of each diagonal?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Here is your rhombus, with the 60� angle at A:

In any rhombus, ABD would be an isosceles triangle, the angles at B and D being congruent. In this case, all 3 angles in ABD are congruent, measuring 60�. So it is really equilateral, and AB=BD=8m is the length of the short diagonal BD.
You can use Pythagoras theorem to find the length of the other diagomal. The diagonals are perpendicular and divide the rhombus into four right triangles. The short side of those triangles is half of BD, measuring 4m. The hypotenuse is the side of the rhombus measuring 8m. The long leg of the triangles measures (in m)

The long diagonal measures twice that, .
You could also work with the trigonometric functions applied to the right triangles, figuring that they have 30� angles at A and C.
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