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