Finding distance from point to line

Question

Knowing the position of 3 points($A, B, C$) , how can I get the distance from $A$ to the line $\overline {BC}$ if I know the angle?

Answer 1

If you have the positions as vectors, compute $\frac{|(A-B)\times (C-B)|}{|C-B|}$.

Answer 2

If the equation of line $BC$ is $$ax+by+c=0$$ and $$A=(x_0,y_0)$$ then $$d(BC,A)=\frac{|ax_0+by_0+c|}{\sqrt{a^2+b^2}}$$