# Calculate Third side of Triangle puzzle?

Given two sides with length 7 cm and 9 cm and angle between them is 25 degrees. Calculate the third side length of the triangle.

**Solution:**

**Mathematical proof:**

Based on the data given , you can calculate the height of the triangle as shown in the above figure.

b side can be split into acosθ and b- acosθ

Applying law of right angled triangle

Expanding the terms we get:

Replace the terms, we get:

**Java Program**

package com.testingdocs.examples; public class TriangleThirdSide { double a; double b; double angle; public TriangleThirdSide(double a, double b, double angle) { this.a=a; this.b=b; this.angle=angle * Math.PI /180; } public double findC() { return Math.sqrt( a*a + b*b - (2*a*b* Math.cos(angle))); } public static void main(String[] args) { TriangleThirdSide triangle= new TriangleThirdSide(7.0,9.0,25.0); double c = triangle.findC(); System.out.println("Third side of the Triangle = "+ String.format( "%.2f", c ) + " cm"); } }

Answer:

Third side of the Triangle = 3.98 cm

public TriangleThirdSide(double a, double b, double angle) { this.a=a; this.b=b; this.angle=angle * Math.PI /180; }

The class constructor takes the values of known sides a , b and the angle between the sides i.e θ . We can create a new Triangle using the new operator as shown below:

Example : new TriangleThirdSide(7.0,9.0,25.0);

Method findC() calculates the third side using the mathematical proof and the formula shown above.