An isosceles triangle - Math Central

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Question from Kim, a student:

I am given the length of the two legs of an isosceles triangle (8),
and the base angles are 30 degrees...I am asked to find the area of
the triangle with only this information

Hi Kim,
A picture of our triangle is a good place to start,

triangle

In Euclidian geometry, the angles of any triangle add up to 180^o.

Therefore, the missing angle is 120^o.

Now imagine we drew a line which cut the big angle in half. We can create two identical (why?) triangles.

triangle

What is the missing angle?
Our new triangles are the so-called “30-60 triangle”, what are the lengths of this ‘special’ triangle’s sides? What are the lengths of the missing sides for the triangle above? What is the formula for the area of a triangle?
Hope this helps.
Tyler

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