SOLUTION: In a Triangle abc what is the distance between the midpoint of bc and the foot of the perpendicular from a to bc, if the length of the sidesof bc,ca and ab are 5cm,7cm,6cm respecti

Question 881678: In a Triangle abc what is the distance between the midpoint of bc and the foot of the perpendicular from a to bc, if the length of the sidesof bc,ca and ab are 5cm,7cm,6cm respectively
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!

Let M be the midpoint of BC
Let F be the foot of the perpendicular from A to BC



We find cos(B) by using the law of cosines on triangle ABC











From right triangle ABF,









Since BC=5 and M is the midpoint of BC, and BC = 5,

BM = half of 5 or 
 
FM = BM - BF =  =  =  = 1.3

Edwin

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