# Thread: area of triangle and sine theta.

1. ## area of triangle and sine theta.

Area of triangle = 1/2 * product of two sides * sine angle.

Can anyone explain the logic of having sine angle in the formula? Please explain in such a way that I don't need to memorize this formula rather derive myself.

2. ## Re: area of triangle and sine theta.

You already know that \displaystyle \begin{align*} A = \frac{1}{2}b\,h \end{align*}.

But if you look at the left-hand right-angle triangle, we can see that from the point of view of angle C, the opposite side is h and the hypotenuse is a.

So \displaystyle \begin{align*} \sin{(C)} = \frac{h}{a} \implies h = a\sin{(C)} \end{align*}.

Thus \displaystyle \begin{align*} A = \frac{1}{2}b\,h = \frac{1}{2}a\,b\sin{(C)} \end{align*}.

3. ## Re: area of triangle and sine theta.

You are awesome!