SOLUTION: Two altitudes of an isosceles triangle are equal to 20 cm and 30 cm . Determine the base angles of the triangle.

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Question 516290: Two altitudes of an isosceles triangle are equal to 20 cm and 30 cm . Determine the base angles of the triangle.
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!


CE = 20, AD = 30

Right triangles ABD and CEB are similar, so

 =  

 =  = 

 = 

BC = AB

BD = BC = ŚAB = AB

By the Pythagorean theorem

BDČ + ADČ = ABČ

(AB)Č + 30Č = ABČ

ABČ + 900 = ABČ

Multiply through by 9

ABČ + 8100 = 9ABČ

8100 = 8ABČ

 = ABČ

 = ABČ

 = ABČ

 = AB

sin(B) = 

sin(B) =  = 30ś = 30Ś =  = .9426090416 

B = sin-1(.9428090416) = 70.52877937°

Edwin
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