Question

Two opposite sides of a parallelogram each have a length of `12`. If one corner of the parallelogram has an angle of `(5 pi)/6` and the parallelogram's area is `24`, how long are the other two sides?

Answer 1

4

Explanation:

`A = bh`

`A = 24`
`b = 12`
`=> h = 2`

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`pi = 180^o`

`=> 5pi/6 = 150^o`

Since we are dealing with a parallelogram, adjacent interior angles have a sum of `180^o`

`=>` other interior angle is `30^o`

If we draw an imaginary segment connecting the bases, we will have a 30-60-90 triangle with the side opposite `30^o` having a length of 2 (i.e. the parallegram's height) and the hypotenuse being the parallelogram's other side.

The sides of a 30-60-90 triangle have the ratio `1:sqrt3:2`.
Since the side opposite `30^o` is 2, the hypotenuse should be 4.