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In triangle PQR, PQ=13, QR=14, and PR=15. Let M be the midpoint of QR. Find PM.

 Jul 18, 2021
 #1
avatar+26396 
+2

In triangle PQR, PQ=13, QR=14, and PR=15.
Let M be the midpoint of QR.
Find PM.

 

cos Rule:
152=132+14221314cos(Q)21314cos(Q)=132+14215221314cos(Q)=140|:21314cos(Q)=70(1)

 

cos Rule:
PM2=132+(142)2213142cos(Q)PM2=132+(142)21314cos(Q)1314cos(Q)=132+(142)2PM21314cos(Q)=132+72PM21314cos(Q)=218PM2(2)

 

(1)=(2):70=218PM2PM2=21870PM2=148PM2=437PM2=237

 

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 Jul 18, 2021
 #2
avatar+26396 
+2

Sorry, There is a typo!

 

PM=237

 

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heureka  Jul 19, 2021
 #3
avatar+1641 
+3

In triangle PQR, PQ=13, QR=14, and PR=15. Let M be the midpoint of QR. Find PM.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PM = [sqrt(2 * 132 + 2 * 152 - 142)] / 2

 

PM = 12.16552506

 

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 Jul 19, 2021

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