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In \($\triangle PQR$\), we have PQ = QR = 34 and PR = 32. Point M is the midpoint of \(\overline{QR}\). Find PM. Please help fast!

Guest Aug 21, 2018
edited by Guest  Aug 21, 2018
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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 :

 

 

cool cool cool

CPhill  Aug 22, 2018

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