Given: △FKL, FK = a

m∠F=45°, m∠L=30°

Find: FL

The sum of angles of a triangle is 180°, so m∠K = 180° - 45° - 30° = 105°.

The Law of Sines tells you

... FL/sin (∠K) = FK/sin (∠L)

Solving for FL, we get

... FL = FK·sin (∠K) / sin (∠L)

... FL = a·sin (105°) / sin (30°) = a·sin (105°) / (1/2)

... FL = 2a·sin (105°) ≈ 1.93185a