Hello, Hanga!

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!

Code:

A * - - - - - * - - - - - * B
/ \ / \ /:
/ \ / \ / : _
1 / \ / \ / : ½√3
/ \ / \ / :
/ 60° \ / \ / :
* - - - - - * - - - - - * - - +
D 1 1 C ½ E

Draw diagonal

It can be seen that is a right triangle

. . with:

Hence: .

Draw diagonal

In right triangle

. .

Therefore: .