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In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
 

 Jun 24, 2024
 #1
avatar+129725 
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cos RMP  = -cos QMP

 

Law of Cosines

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

PR^2 = RM^2 + PM^2 - 2(RM * PM) (-cos QMP)

 

18^2 = 12.5^2 + PM^2 - 2(12.5*PM)cos (QMP)

23^2 = 12.5^2 + PM^2 +2(12.5 * PM)cos(QMP)        add these

 

853 = 312.5 + 2PM^2

 

[853 -312.5] / 2   = PM^2

 

540.5 / 2  = PM^2

 

PM = sqrt [ 540.5/2 ] ≈ 16.44

 

 

cool cool cool

 Jun 25, 2024

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