Question

find the perimeter of an isosceles triangle whose base is 20cm and the vertex angle is 120 degrees.

Answer 1

draw an altitude. That will give you two right triangles that are 30-60-90 degrees.

Since the sides of those triangles are in the ratio of 1:√3:2, and you have the long leg as half the base, or 10cm, the hypotenuse (the side of the isosceles triangle) has length 20/√3.

So, the triangle has perimeter

20 + 20√3 + 20√3