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

 

 Apr 23, 2024
 #1
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Law of Cosines

 

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)

 

Simplify

 

(18^2 - 12.5^2 - PM^2 ) /  [ -25 PM ]   = cos (QMP)

[23^2 - 12.5^2 - PM^2 ] / [ 25 PM =  cos (OMP)

 

Equate cosines  and simplify

 

- [ 167.75 - PM^2 ]   =  [372.75 - PM^2]

 

2PM^2  = 540.5

 

PM^2  = 270.25

 

PM =sqrt [ 270.25]  ≈  16.44

 

 

cool cool cool

 Apr 23, 2024

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