Hello, snezic!

If we're allowed to use trig, I have a solution.

(And I'm sure someone will find a shorter or neater one.)

We have a triangle , that has a right angle at the vertex

We draw the altitude

Now we draw two lines from point :

. . parallel to parallel to

Prove that: .

Code:B o | * | * | θ * D E o - - - - - o | x /: * | / : * | / : * | / θ : * | / : * y| /v :y * | / : * | θ / : * | / : * | / : * |/ : θ * C o - - - - - o - - - - - - - - - - - - - - - - - o A x F

Note that all the right triangles are similar.

. .

Substitute [3] and [4] into [1] and [2]: .

. . Therefore: .