How do I find a point given an angle and distance to it?

Question

I'm working on a school project creating a tank team in the programming game Robocode. (It's a tank battle game with self-programmed bots, in Java).

I'm programming a scout bot that scans, finds enemies and reports them to the commander bot. I only have the distance and angle to the scanned enemy bot. How can I find its X,Y-position using only these known variables?

Here's a diagram:

Answer 1

Simple?

NewPos = new Vector2(825 * sin(85 degrees), 825 * cos(85 degrees));

Most libraries use radians not degrees, so:

radians = degrees * PI / 180

If you want the coordinates in the world reference frame, you will need to get the direction of the Tank, subt add the centre Tanks origin to the result:

NewDir = TankDir + 85;
NewPos = new Vector2(825 * sin(NewDir), 825 * cos(NewDir));
NewWorldPos = NewPos + TankWorldPos

Answer 2

I think this will be enough if you don't use scale.

float Angle = RotationTankA - RelativeAngle;

PosTankB = PosTankA + new Vector2(cos(Angle), sin(Angle)) * Distance;

Answer 3

I have just made up an example in C#/XNA and got it to work perfectly.

Here is the current function

public Vector2 GetPosition(Vector2 CurPos, float angle, float distance)
        {
            //Get SOH
            float op = (float)Math.Sin(angle) * distance;
            //Get CAH
            float ad = (float)Math.Cos(angle) * distance;
            //Add to old Vector
            return (CurPos + new Vector2(ad, op));
        }

Note that angle 0 means that the CurPos Tank Sprite is pointing right, In the example I made, I simple used the Left and Right arrow keys to + or - the current angle, and when drawing would simple use...

        batch.Draw(BaseSprite, Position, null, Color.White, BaseRotation, new Vector2(BaseSprite.Width / 2, BaseSprite.Height / 2), 1, SpriteEffects.None, 0);

Obviously this is in C#, but i'm sure it wouldn't be too hard to convert to Java, seeing as both languages are quite similar anyway.