Determine the coordinates of a segment

Question

How can I use atan2 to determine the coordinates where a segment ends, knowing the coordinates where it starts (x, y), the angle of the segment and the length of the segment?

Can you tell me a solution it doesn't have to be only with atan2...

Answer 1

You have a right angled triangle and you can assume that the point A is at (x,y), this is much easier to explain with the use of some diagrams:

Now we know what the value for c is already because this is the length of the segment and we want to know the values for a and b because the final point is at (x+b, y+a)

From trigonometry we know what the relations between the angles and the ratios of the sides are

sin(theta) = opposite/hypotenuse and cos(theta) = adjacent/hypotenuse

Substituting in the values we know we get:

sin(theta) = opposite/c
c = opposite * sin(theta)

and

cos(theta) = adjacent/b
b = adjacent * cos(theta)

We know that the end point is at (x+b, y+a) which given the values for the edges we found is (x+adjacent * cos(theta), y+opposite * sin(theta))