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

 

 Mar 21, 2024
 #1
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Law of Cosines

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

23^2  =18^2 + 25^2  - 2(18 * 25) cos (PQR)

[23^2 - 18^2 - 25^2 ] / [ -2 * 18 * 25 ] =  cos (PQR)

7/15 = cos (PQR)

 

Law of Cosines again

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

PM^2  = 18^2 +(12.5)^2  - 2 (18 * 12.5)(7/15)

PM^2 = 270.25

PM = sqrt (270.25)  ≈  16.44

 

cool cool cool

 Mar 21, 2024

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