If angleB and angleQ are acute angles such that sin B=sin Q, then prove that angle B= angle Q.(with explanation)

If angleB and angleQ are acute angles such that sin B=sin Q, then prov

1.	If angleB and angleQ are acute angles such that sin B=sin Q, then prove that angle B= angle Q.(with explanation)
Answer» HAT ∠B and ∠Q are acute ANGLE andsinB=sinQ__ (A)From ΔACB and ΔPRQsinB= AB/AC __(1)sinQ= PQ/PR ___(2)From equation (A)sinB=sinQAB/AC = PQ/PR let AB/AC = PQ/PR =k∴ PR/AC = PQ/AB =k __(3)Now,AC=k×PRAB=k×PQFrom ΔACBBy Pythagoras THEOREM AB2 =AC2+BC2(k×PR)2 =(k×PQ)2 +BC2 ⇒k2 ×PR2 =k2 ×PQ2 −BC2 ⇒BC2 =k2 ×PR2 −k2 PQ2=k2 [PR2 −PQ2 ] ∴BC= √k2[PR2 −PQ2 ]From ΔPRQBy Pythagoras theorem PQ2 =PR2 +QR2 ⇒QR2 =PQ2 −PR2 ∴QR= √PQ2 −PR2Consider thatQR/BC =k __(4)From equation (3) and (4) to, PR/AC = PQ/AB = QR/BC Hence, ΔACB∼ΔPRQ (sss similarity)∠B=∠Qmark me as brainlist