If I know that the sides of a parallellogram is 1 and 2, and that one angle is 60°,
can I, using plain Euclidean Geometry, calculate the diagonals exactly? . . . . Yes!
We have parallelogram ABCD with: .
This parallelogram can be divided into four equilateral triangles!
A * - - - - - * - - - - - * B
/ \ / \ /:
/ \ / \ / : _
1 / \ / \ / : ½√3
/ \ / \ / :
/ 60° \ / \ / :
* - - - - - * - - - - - * - - +
D 1 1 C ½ E
It can be seen that is a right triangle
. . with:
In right triangle