From Rusty

For a work project: what is the formula to determine the length of the third side of a 45 degree Isosceles triangle?

Thank you.

Hi Rusty,

In the diagram below s is the length of the side you know and x is half the length of the third side of the triangle.

Since the angle CAB is 45 degrees the angle CAD is 22.5 degrees. Thus

sin(22.5) =  ^x/_s

and thus

x = s sin(22.5)

Hence the length of the third side is

2x = 2 s sin(22.5) = 2 s 0.38268 = 0.76537 s

Penny