Question 1185238

The measure of each base angle of an isosceles

triangle is 30, and each of the two congruent sides has
length 14. What is the area of the triangle?
<pre>Use the formula for the area for any NON-RIGHT triangle: {{{matrix(1,3, Area, "=", (1/2)ac*sin (C))}}}, with &#8737 C being the angle between sides "a" and "b". 
&#8737 C = 180 - 2(30) = 180 - 60 = 120<sup>o</sup>.

This gives us: {{{matrix(1,5, Area, of, triangle, "=", (1/2)(14)(14) * sin (120^o))}}}
                                  {{{highlight_green(matrix(3,2, "=", (1/2)(14)(14) * (sqrt(3)/2),
"=", (1/4) * 14(14)sqrt(3),
"=", highlight(49sqrt(3))))}}}</pre>