In \($\triangle PQR$\), we have PQ = QR = 34 and PR = 32. Point M is the midpoint of \(\overline{QR}\). Find PM. Please help fast!
+128475
OK.... since M is the mid-point of QR then MR = 17
This triangle is isosceles so if we let QS be the altitude....then this altitude will bisect PR..
So....SR = 16
And the cosine of angle QRS = SR/ QR = 16/34 = 8/17
Using the Law of Cosines
PM^2 = MR^2 + PR^2 - 2(MR)(PR)cos(QRS)
PM^2 = 17^2 + 32^2 - 2(17)(32) (8 /17)
PM^2 = 1313 - 16*32
PM^2 = 1313 - 512
PM = sqrt (1313 - 512)
PM =sqrt (801) = sqrt ( 9 * 89) = 3 sqrt (89) ≈ 28.3 units
Here's a pic :
