SOLUTION: The congruent angles of an isosceles triangle are 1/3of the vertex angle. Find the area of the congruent sides are 14in

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Question 963851: The congruent angles of an isosceles triangle are 1/3of the vertex angle. Find the area of the congruent sides are 14in
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
x, degree measure of vertex angle;
2%28x%2F3%29%2Bx=180
2x%2B3x=3%2A180
5x=3%2A180
x=3%2A2%2A5%2A18%2F5
x=6%2A18
x=108

The base angles each are 108%2F3=36 degree.

Altitude from vertex to the base cuts the isosceles triangle into TWO congruent right triangles with hypotenuse 14 inches, from the given descriptive question. This altitude segment is opposite the 36 degree angle. At the vertex location is a 54 degree angle. DRAW that much of this to show the angles and segments.

Now you want to know the size of the altitude.
Altitude is 14%2Acos%2854%29;
The half of the isosceles base would be 14%2Acos%2836%29.
That means the entire base of the isosceles triangle is 28%2Acos%2836%29.
Using area formula for a triangle, the area would be %281%2F2%29%28base%29%28altitude%29, which you can fill-in and compute.