Calculate the area of the triangle ABC if AB=10, AC=20, sinA=sqrt3/2.

We'll have many formulas to compute the area of a
triangle.

The one which is very oftenly used
is:

S = base*height/2

Another
one, less applied, is:

S =
a*b*sin(a,b)/2

Knowing the values of the lengths of the
sides AB and AC, also the measure of an angle of the triangle, we'll use the formula of
the area:

S = AB*AC*sin
A/2

S = 10*20*sinA/2 = 100*sin
A

But sin A = sqrt3/2

S =
100*sqrt3/2

We'll divide by 2 both denominator and
numerator:

S =
50*sqrt3

S = 86.60 square
units