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In isosceles triangle ABC, we have AB=AC=4. The altitude from B meets AC at H. If AH=2(HC) then determine BC.

 Sep 11, 2023
 #1
avatar+128397 
+1

           A

 

 

 

                 H

 

B                   C

 

AH = (2/3) (4) =  8/3

HC = 4/3

 

Triangle BAH  is right with BHA = 90

 

So

 

BH = sqrt (AB^2 - AH^2)  = sqrt ( 4^2 - (8/3)^2)  = sqrt [ 16 - 64/9 ]  = sqrt [ (144 - 64) ] / 3 = sqrt (80 ) / 3  

 

Triangle HBC is right with  BHC = 90

 

BC  =sqrt ( BH^2 + HC^2)  = sqrt ( (sqrt (80) / 3)^2  + (4/3)^2 )  = sqrt [ 80/9 + 16/9]  = sqrt ( 96) / 3 = 

 

4sqrt (6) /  3

 

 

cool cool cool

 Sep 11, 2023
 #2
avatar+6 
0

Is the answer 4sqrt (6) / 3   

Vampire Survivors

 Sep 12, 2023

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