If sides A and B of a triangle have lengths of 9 and 12 respectively, and the angle between them is $(pi)/3$ , then what is the area of the triangle?

Question

1798 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-18T00:30:24

$27sqrt(3)$

Taking a look at the triangle, we have something like the following:

enter image source here

From the right triangle containing the angle $pi/3$ we have

$sin(pi/3) = h/9 => h = 9sin(pi/3) = (9sqrt(3))/2$

Then, applying the area formula $A = 1/2bh$

$"area" = 1/2(12)((9sqrt(3))/2) = 27sqrt(3)$

If sides A and B of a triangle have lengths of 9 and 12 respectively, and the angle between them is (pi)/3(pi)/3, then what is the area of the triangle?