SOLUTION: How do you find the area of a parallelogram with sides 8 and 14 and an included angle of 60 degrees?

Question 253190: How do you find the area of a parallelogram with sides 8 and 14 and an included angle of 60 degrees?
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
Draw your parallelogram with sides 8 and 14 with angle of 60 degrees with the 60 angle at the base on the left.
If one angle is 60 the opposite angle is also 60.
The remaining angles are 120 each.
Now draw the height (altitude) from the 120 angle to the base .
We now have a right triangle with angles 30 60 90. We know that the sides in a 30 60 90 triangle are proportioned 1:sqrt(3):2
Now since the hypotenuse is 8 the triangles proportions are multiplied by 4.
so the altitude is 4sqrt(3)
We are not told where the 60 degree angle is.
I choose to make the base 14 and the altitude is 4sqrt
So the area is base times height which is 14*4sqrt(3)=64sqrt(3)
If the base is 8 then the height is 7sqrt(3) and the area is 8*7sqrt(3) or 56sqrt(3)
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