Question

Two sides of a triangle are x units and y units in length. The angle between them is theta. Prove that the area of the triangle is 1/2xysin(theta).


I'm not sure how to do this question, I tried drawing a picture but I'm still not understanding it.

Answer 1

draw a perpendicular from side x to side y, let it be h
Area of triangle
= (1/2)base x height
= (1/2) y h

but sinØ = h/x
h = xsinØ

so area =(1/2) y xsinØ
= (1/2)xy sinØ