Using rotation to set an objects position

I have my character run into an object and when they touch I want the character to be moved (instantaneously) using transform.position based on the transform.eulerAngles.y of the object touched.

So in other words if the transform.eulerAngles.y = 90 the object (which is an arrow essentially) would be pointing to the right, and when touched would teleport the character about 10 units to the right.

I keep thinking this might involved the unit circle (sine and cos and whatnot) but I can’t quite figure it out. Any ideas, thanks.

The easiest way would be to use the built in transform methods forward, back, right, top, etc. Just set up your arrow so that, say, it points towards +x in local coordinates. Then use

Vector3 newPos = oldPos + arrowTransform.forward * distanceToMove;