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) About Me  (Show Source):
You can put this solution on YOUR website!


CE = 20, AD = 30

Right triangles ABD and CEB are similar, so

CE%2FAD = BC%2FAB 

CE%2FAD = 20%2F30 = 2%2F3

BC%2FAB = 2%2F3

BC = 2%2F3AB

BD = 1%2F2BC = 1%2F2Ś2%2F3AB = 1%2F3AB

By the Pythagorean theorem

BDČ + ADČ = ABČ

(1%2F3AB)Č + 30Č = ABČ

1%2F9ABČ + 900 = ABČ

Multiply through by 9

ABČ + 8100 = 9ABČ

8100 = 8ABČ

8100%2F8 = ABČ

2025%2F2 = ABČ

sqrt%282025%2F2%29 = ABČ

45%2Fsqrt%282%29 = AB

sin(B) = AD%2FAB

sin(B) = 30%2F%2845%2Fsqrt%282%29%29 = 30ś45%2Fsqrt%282%29 = 30Śsqrt%282%29%2F45 = 2sqrt%282%29%2F3 = .9426090416 

B = sin-1(.9428090416) = 70.52877937°

Edwin