Assume every side length of a triangle ABC is more than 2 and two of its angles are given by ∠ABC=57∘ and ACB=63∘. Point P is chosen on side BC with BP:PC=2:1. Points M,N are chosen on sides AB and AC, respectively so that BM=2 and CN=1. Let Q be the point on segment MN for which MQ:QN=2:1. Find the value of PQ. Your answer must be in simplest form. geometrytrigonometryratiosimilar triangles