Answer:
PQ = [tex]PM\cos MPQ + MQ\cos MQP=2PM\cos MQP[/tex]
Step-by-step explanation:
given MQR = 60, PQR = 75
MQP = 75 -60= 15[tex]QR = ((18(1+\cos 30))^{2}-(2\cos 15)^{2})^{\frac{1}{2}}[/tex]
WE KNOW THAT MQR +QRM +QMR = 180
MPQ = MQP AS ANGLE OPPOSITE TO EQUAL SIDES ARE EQUAL
THEREFORE QMR = 90 - 60 = 30
therefore PQM = 75 - 60 = 15
PM = PQ because M is the mid point
therefore PR = PM + [tex]MQ\cos QMR[/tex]
PR = [tex]18(1+\cos 30)[/tex]
[tex]QR = (PR^{2}-PQ^{2}))^{\frac{1}{2}}[/tex]
PQ = [tex]PM\cos MPQ + MQ\cos MQP=2PM\cos MQP[/tex]
