Question

If sides A and B of a triangle have lengths of 1 and 2 respectively, and the angle between them is `(2pi)/3`, then what is the area of the triangle?

Answer 1

The area is `sqrt3/2`; or, *0.866 *

Explanation:

You'll need the sine rule for area of the triangle.
The formula is:
Area of the `triangleABC = 1/2*a*b*sin C`
This drawing(sorry if it's clumsy) will show what I mean :

Here, `angle C = (2pi)/3`
`sin C= sqrt 3/2`
Plugging in the values;
a=1;
b=2;
`sin {(2pi)/3} = sqrt3/2`
Area of #triangle ABC = 1/2*1*2*sqrt3/2 =sqrt3/2#
*Do not forget to give the units...