Homework Help: Finding angles of a parallelogram.

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1. Oct 2, 2015

tiggertime

1. The problem statement, all variables and given/known data
This question has popped up recently and I was completely stumped. How to find the angles of a parallelogram given only area and the length of the diagonals? I'm trying to find a generic solution or formula that works for a non-rhombus.

2. Relevant equations

3. The attempt at a solution

Parallelogram and Triangle Laws
Setting angle variable equal height(sin(angle variable))

2. Oct 2, 2015

HallsofIvy

The area of a parallelogram is "base times height". "Base" is the length of one side, b. The height is the length of perpendicular from a vertex to the base. Given angle $\theta$ the height is the "opposite side" while the length of that side, a, is the hypotenuse, h, so $h= a sin(\theta)$ The area is $ab sin(\theta)$.

3. Oct 3, 2015

tiggertime

I still don't understand how to obtain sides a and b from the diagonal lengths since there are no right angles to use Pythagoras.

4. Oct 3, 2015

insightful

I got a solution using the Law of Cosines with the angle of intersection of the diagonals to get the lengths of the sides.

5. Oct 3, 2015

tiggertime

So you were given the angle of intersection? How do you find the sides without that information? I tried substituting A=absinθ into the equation, after working through sine changes, but the solution keeps cancelling out.

6. Oct 3, 2015

insightful

No, you can use some simple trig in one quadrant of the parallelogram to get the angle (in terms of A and diagonals d1 and d2). Remember, each quadrant has 1/4 the total area A.

Last edited: Oct 3, 2015