Ray - 3d triangle intersection test

Game Mechanics
#1

I have written simple ray-triangle intersection code based on this two tutorials: http://graphics.stanford.edu/courses/cs348b-98/gg/intersect.html, http://www.scratchapixel.com/lessons/3d-basic-lessons/lesson-9-ray-triangle-intersection/ray-triangle-intersection-geometric-solution/. It works perfectly for triangles with all points y=0, but when any (or all) points have another y values then it does not work properly.

Here is the code for intersection (glColor calls added for debugging): http://www.java-gaming.org/?action=pastebin&id=676

Triangle:

package intersection;

import org.lwjgl.util.vector.Vector3f;

public class Triangle {

    public Vector3f p0;
    public Vector3f p1;
    public Vector3f p2;
    
    public Triangle(Vector3f p0, Vector3f p1, Vector3f p2) {
        this.p0 = p0;
        this.p1 = p1;
        this.p2 = p2;
    }
    
}

Ray:

package intersection;

import org.lwjgl.util.vector.Vector3f;

public class Ray {

    private Vector3f start;
    private Vector3f dir;
    private float angleX;
    private float angleY;
    
    public Ray(float x, float y, float z, float angleX, float angleY) {
        start = new Vector3f(x, y, z);
        dir = new Vector3f();
        this.angleX = angleX;
        this.angleY = angleY;
        updateDir();
    }
    
    Vector3f getStartVector() {
        return start;
    }
    
    public float getStartX() {
        return start.x;
    }
    
    public float getStartY() {
        return start.y;
    }
    
    public float getStartZ() {
        return start.z;
    }
    
    Vector3f getDirVector() {
        return dir;
    }
    
    public float getDirX() {
        return dir.x;
    }
    
    public float getDirY() {
        return dir.y;
    }
    
    public float getDirZ() {
        return dir.z;
    }
    
    public float getAngleX() {
        return angleX;
    }
    
    public float getAngleY() {
        return angleY;
    }
    
    public void setPosition(float x, float y, float z) {
        start.x = x;
        start.y = y;
        start.z = z;
        updateDir();
    }
    
    public void setAngle(float angleX, float angleY) {
        this.angleX = angleX;
        this.angleY = angleY;
        updateDir();
    }
    
    public void setPositionAndAngle(float x, float y, float z, float angleX, float angleY) {
        start.x = x;
        start.y = y;
        start.z = z;
        this.angleX = angleX;
        this.angleY = angleY;
        updateDir();
    }
    
    private void updateDir() {
        dir.x = (float)(Math.cos(angleY)*Math.sin(angleX));
        dir.y = (float)-Math.cos(angleX);
        dir.z = (float)(Math.sin(angleY)*Math.sin(angleX));
    }
    
}

Why this code works incorrectly? I am trying to find bug, but don’t found everything since 2 days. :-\