In triangle PQR, PQ=13, QR=14, and PR=15. Let M be the midpoint of QR. Find PM.
In triangle PQR, PQ=13, QR=14, and PR=15.
Let M be the midpoint of QR.
Find PM.
cos Rule:
152=132+142−2∗13∗14∗cos(Q)2∗13∗14∗cos(Q)=132+142−1522∗13∗14∗cos(Q)=140|:213∗14∗cos(Q)=70(1)
cos Rule:
PM2=132+(142)2−2∗13∗142∗cos(Q)PM2=132+(142)2−13∗14∗cos(Q)13∗14∗cos(Q)=132+(142)2−PM213∗14∗cos(Q)=132+72−PM213∗14∗cos(Q)=218−PM2(2)
(1)=(2):70=218−PM2PM2=218−70PM2=148PM2=4∗37PM2=2√37