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In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11

 
 Oct 16, 2025
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          P

     5           8

Q         M           R

     5.5       5.5

 

 

Law of Cosines  (twice)

[QP^2 - QR^2 - PR^2] /[-2* QR * PR] =  cos PRQ

[ 25 - 121 - 64] / [-2 * 11 *8 ] = cos PRQ  = 10/11

 

PM^2 = MR^2 + PR^2  - 2 (MR * PR) *cos (PRQ)

PM^2  = 30.25 + 64 - 2[5.5 * 8]* (10/11)

PM ^2  =14.25

PM =sqrt [14.25] ≈ 3.77

 

cool cool cool

 9 hours ago

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