An isosceles triangle has an area of 30 cm2, and the angle between the two equal sides is 5π/6. Find the length of the two equal sides. (Round your answer to one decimal place.)

Answer 1

First, bisect the angle between the two equal sides, splitting the isosceles triangle into two congruent right triangles. If the height of one of these triangles is h, and the base is b, then the area is h*b/2... and the area of the original triangle is h*b, which equals 30.

If x is the length of the two equal sides, then b/x is sin(5pi/12), and h/x is cos(5pi/12), since 5pi/12 is half of the angle that was bisected when forming those two right triangles. Now using h*b=30, substitute h=x*cos(5pi/12) and b=x*sin(5pi/12), then solve for x.