Question 1185238
h = the altitude of the isosceles triangle.
sin(30) = h/14
h = 14 * sin(30) = 14 * 1/2 = 7
cos(30) = (b/2) / 14
b/2 is half the base of the isosceles triangle.
b is the base of the isosceles triangle.
cos(30) = sqrt(3)/2
this gets you:
sqrt(3)/2 = (b/2) / 14
solve for b/2 to get:
b/2 = 14 * sqrt(3)/2 = 7*sqrt(3).
b = 14 * sqrt(3)/2
the area of the isosceles triangle = 1/2 * b * h which is equal to 1/2 * 14 * sqrt(3) * 7 which is equal to 7 * sqrt(3) * 7 which is equal to 49 * sqrt(3).
the area of the triangle is equal to 49 * sqrt(3) square units which is equal to 84.87048957 square units.