Question

Ray MN is the bisector of segment KL. KL = KM and KM = 5 cm. Find KN.

Answer 1

$$KM = KL = ML = MN$$ $$\angle KML = 60{}^{\circ}$$ $$\angle KMN = 30{}^{\circ}$$$$\angle KMA = 15{}^{\circ}$$ $$\frac{AK}{5} = \sin(15{}^{\circ}) \quad AK = 5\sin(15{}^{\circ}) \quad KN = 10\sin(15{}^{\circ}) = 2.6\,cm$$