PART A
By the sine law, we know that
sin(<A)/A is sin(<B)/B which is equal to sin(<C)/C.
THEREFORE,
sin(<120)/22m = sin(<30)/x
We need to isolate x.
x= 22m * (sin 30 degrees/sin 120 degrees)
x=12.7017059222m
Since we have an isosceles triangle, each side is about 12.7m.
PART B
We need to find the area of the triangle.
The formula for area is base x height /2 .
Our height we need to find out with the pythagorean theorem. half of our triangle means a length of the triangle at 11m.
a^2+b^2=c^2.
Therefore, (12.7)^2=11^2+x^2
Our height is 6.35084703891 m.
Base x height /2= area
area= 6.35084703891 m * 11 m / 2= 34.929658714m.
This is our area.