MyProgram.java

public class MyProgram
{
    public static void main(String[] args) throws RuntimeException
    {
        Triangle[] triangles = new Triangle[] {
            new Triangle(1,1,1),
            new Triangle(3,3,5),
            new Triangle(8,9,8),
            new Triangle(2,2,2),
        };
        Triangle referenceTri = new Triangle(1,1,1);
        for(Triangle t : triangles) {
            System.out.println("== Start new triangle ==");
            System.out.println(t);
            System.out.println("Triangle area: "+t.getArea());
            System.out.println("Triangle perimeter: "+t.getPerimeter());
            System.out.println("Triangle's largest angle: "+t.getLargestAngle());
            System.out.println("Triangle's area (using law of cosines): "+t.getAreaTrig());
            System.out.println("Triangle's area greater than or equal to a 1,1,1 triangle: "+t.areaGreaterThan(referenceTri));
        }
    }
}

Triangle.java

public class Triangle {
    private int a; //smallest side
    private int b; //middle side
    private int c; //longest side
    //Creates a new triangle with the sicdes specified.
    public Triangle(int a, int b, int c) throws RuntimeException {
        int s,m,l;
        //We need to find out which sides are small, medium, and large.
        //This chain of if-elses does that, and sets s, m, and l, to those sides respectively.
        if(a <= b && a <= c) {
            //a is the smallest.
            s = a;
            //The medium option is now between b and c, so compare them to find out.
            if (b <= c) {
                m = b;
                l = c;
            } else {
                l = b;
                m = c;
            }
        } else if (b <= c) {
            //b is the smallest.
            s = b;
            //between a and c now.
            if(a <= c) {
                m = a;
                l = c;
            } else {
                m = c;
                l = a;
            }
        } else {
            //c is the smallest.
            s = c;
            //between a and b now.
            if(a <= b) {
                m = a;
                l = b;
            } else {
                m = b;
                l = a;
            }
        }
        if(s + m <= l) {
            //The sum of the two smallest sides must exceed the longer side in order to be valid.
            throw new RuntimeException("Invalid values for triangle");
        }
        this.a = s;
        this.b = m;
        this.c = l;
    }
    public Triangle() {
        this(1, 1, 1);
    }
    
    public String toString() {
        return String.format("Triangle with sides %d, %d, %d", a, b, c);
    }
    
    //Returns the triangle's perimeter.
    public int getPerimeter() {
        return a + b + c;
    }
    
    //Returns the triangle's area.
    public double getArea() {
        double s = getPerimeter() / 2.0;
        return Math.sqrt(s * (s - a) * (s - b) * (s - c));
    }
    
    //Returns the triangle's area, using law of cosines to calculate.
    public double getAreaTrig() {
        return 0.5 * a * b * Math.sin(Math.toRadians(this.getLargestAngle()));
    }
    
    //Returns whether this triangle is greater than or equal to another in area.
    public boolean areaGreaterThan(Triangle other) {
        return this.getArea() >= other.getArea();
    }
    
    //Returns the triangle's largest angle in degrees.
    public double getLargestAngle() {
        return Math.toDegrees(Math.acos((Math.pow(c, 2) - Math.pow(b, 2) - Math.pow(a, 2)) / (-2 * a * b)));
    }
}