My problem can be describe by following image:
I know coordinates of an example P
point. Say, they are equal to (8,8)
. I also know the length of a
, b
and c
sides of the triangle which are equal to 10
. Now, how one can calculate the coordinates of ABC
points?
SOLVED (11/3/2016)
Thanks to @EmilioNovati answer to my other question ("How to calculate $B(x_1,y_1)$ when $\alpha$ and $A(x_0,y_0)$ are known?"), I found a solution to my problem with coordinates of triangle vertices.
First lets look at following drawing:
Now, in order to calculate $A(x_A,y_A)$, $B(x_B,y_B)$ and $C(x_C,y_C)$, one can do:
$x_C = x_P + a*cos(\alpha)$,
$y_C = y_P + a*sin(\alpha)$;
$x_A = x_P + a*cos(\alpha+\beta)$,
$y_A = y_P + a*sin(\alpha+\beta)$;
$x_B = x_P + a*cos(\alpha+\beta+\gamma)$,
$y_B = y_P + a*sin(\alpha+\beta+\gamma)$.
Best Answer
Hint:
using elemental geometrical properties of equilateral triangles you can see that:
$$ PC=PA=PB=\frac{10\sqrt{3}}{3} $$
and the distance of $P$ from the sides is half this value.
Can you do from this adding or subtracting such values from the coordinates of $P$ to find the vertices?