SOLUTION: The vertex angle of a triangle is three times the measure of either base angle. Find the area if the measure of the congruent sides are 14 in.

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Question 728416: The vertex angle of a triangle is three times the measure of either base angle. Find the area if the measure of the congruent sides are 14 in.
Answer by mbmodak(32) About Me  (Show Source):
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The vertex angle of a triangle is three times the measure of either base angle. Find the area if the measure of the congruent sides are 14 in.

For Isoselese triangle
base=a
legs=b
base angle=beta
vertex angle=alpha
sum of 3 angles of triangle=180
2*beta+alpha=180
altitud=h S=a*h/2
Area=S S=(b^2/2)*sin alpha degrees

Sum of angles of triangle=180
2*beta+alpha=180
now alpha=3*beta
3*beta+2*beta=180
5*beta=180
beta=180/5=36 degrees
And alpha=3*36=108 degrees

S=a*h/2
S=(b^2/2)*sin alpha
=(14^2/2)*SIN108 b is congruent side
93.1392