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Plz help Im stuck

 

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

 
 Jan 12, 2024
 #1
avatar+128732 
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       P

     

    5             8

 

Q         M              R

            11

 

Law of Cosines

 

PR^2  =  QR^2  + PQ^2  - 2(QR * PQ) cos (PQR)

 8^2 = 11^2  + 5^2  - 2 ( 11 * 5) cos (PQR)

cos (PQR)  =  [ 8^2 - 11^2  - 5^2 ] / [ -2 * 11 * 5]   =  41/55

 

QM  =  11/2 =  5.5

 

Law of Cosines again 

 

PM^2  = QM^2 + PQ^2  - 2 (QM * PO) cos (PQR)

PM^2  = 5.5^2 + 5^2  - 2 ( 5.5 * 5) ( 41/55)

PM = sqrt [ 5.5^2 + 5^2  - 2 ( 5.5 * 5) ( 41/55) ]  ≈  3.77

 

 

cool cool cool

 Jan 12, 2024

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