Question

The lenght of each of the two sides of an isisceles triangle is 10 meters. The angle between the two congruent sides is x. find the area of the triangle as a function of x/2.

Answer 1

First draw a picture. Split the isosceles triangle down the middle of triangle, bisecting the angle x. Now you have divided the isosceles triangle into two right angled triangles, each with area of 1/2 height * base.

So the area of the isosceles is the sum of both of these smaller right angled triangles, or height * base

The base of the right angle triangle is given by base = 10 * sin(x/2)
The height of the right angle triangle is given by height = 10*cos(x/2)

area = 100*cos(x/2)*sin(x/2)