In a polar coordinate system, the vertices of a triangle are at (6,30 degrees), (2, 90 degrees), and (4, 150 degrees). Find the area of this triangle.
+128474 We can convert the polar coordinates to rectangular coordinates
(6,30) = (6cos 30, 6 sin30) = ( 3 √3 , 3) = A
(2, 90) = (0, 2) = B
(4,150) = ( 4cos 150 , 4 sin 150) = (- 2 √3, 2) = C
We can let BC be the base = 2 √3
And the height = 1
So....the area =
(1/2) * (2 √3) (1) = √3 units^2
