Focus on the triangle PQN and triangle SQP, prove that they are similar: PQ=PR, PN is the altitude, so QN=NR=9 PQ of ΔSQP:QN=15:9=5:3 PS:PN=20:12=5:3 ∠PQN=∠SQP (they are the same angle, reflexive property) therefore, according to the SAS similarity theorem, ΔPQN is similar to ΔSQP ∠PNQ=∠SPQ =90 degree therefore, QPS is a right angle.
you may have to reword it depending on what your teacher requires, column proof or paragraph proof.