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 In isosceles triangle ABC, we have AB=AC=4. The altitude from B meets overline{AC} at H. If AH=3(HC) then determine BC.

 

Thanks to all that answered!

 Nov 23, 2019
 #1
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I'm getting BC = sqrt(26).

 Nov 24, 2019
 #2
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Triangle ABH is a right triangle with:
Sides: a = sqrt(7),  b = 3,  c = 4

Area: T = 3.969
Perimeter: p = 9.646
Semiperimeter: s = 4.823

Angle ∠ A = α = 41.41° = 41°24'35″ = 0.723 rad
Angle ∠ B = β = 48.59° = 48°35'25″ = 0.848 rad
Angle ∠ C = γ = 90° = 1.571 rad

 

 

Triangle ABC is an isosceles triangle with:
a =4, b=4, Angle A =41.41 degrees.
Solving for SAS triangle we get:
Sides: a = 4, b = 4, c = 2.828
Or BC =2.828

 Nov 24, 2019
 #3
avatar+2490 
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do some pythagorean theorem... but draw it out first.

 Nov 24, 2019

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