MATHEMATICAL FUNCTIONS, CHARACTERS, AND STRINGS - Introduction to Java Programming: Comprehensive Version - page 123

4.2.6 Case Study: Computing Angles of a Triangle
You can use the math methods to solve many computational problems. Given the three sides
of a triangle, for example, you can compute the angles by using the following formula:

A = acos((a * a - b * b - c * c) / (-2 * b * c))
B = acos((b * b - a * a - c * c) / (-2 * a * c))
C = acos((c * c - b * b - a * a) / (-2 * a * b))

x2, y2

a

B

c

C

x3, y3

A

b

x1, y1

Don't be intimidated by the mathematic formula. As we discussed early in Listing 2.9,
ComuteLoan.java, you don't have to know how the mathematical formula is derived in order
to write a program for computing the loan payments. Here in this example, given the length of
three sides, you can use this formula to write a program to compute the angles without having
to know how the formula is derived. In order to compute the lengths of the sides, we need to
know the coordinates of three corner points and compute the distances between the points.
Listing 4.1 is an example of a program that prompts the user to enter the x- and y-coordinates
of the three corner points in a triangle and then displays the three angles.

L ISTING 4.1

ComputeAngles.java
1 import java.util.Scanner;
2
3 public class ComputeAngles {
4 public static void main(String[] args) {
5 Scanner input = new Scanner(System.in);
6
7 // Prompt the user to enter three points
8 System.out.print( "Enter three points: " );
9 double x1 = input.nextDouble();

enter three points

10 double y1 = input.nextDouble();

11 double x2 = input.nextDouble();

12 double y2 = input.nextDouble();

13 double x3 = input.nextDouble();

14 double y3 = input.nextDouble();

15
16 // Compute three sides
17 double a = Math.sqrt((x2 - x3) * (x2 - x3)
18 + (y2 - y3) * (y2 - y3));
19 double b = Math.sqrt((x1 - x3) * (x1 - x3)
20 + (y1 - y3) * (y1 - y3));
21 double c = Math.sqrt((x1 - x2) * (x1 - x2)
22 + (y1 - y2) * (y1 - y2));
23
24 // Compute three angles
25 double A = Math.toDegrees(Math.acos((a * a - b * b - c * c)
26 / ( -2 * b * c)));
27 double B = Math.toDegrees(Math.acos((b * b - a * a - c * c)
28 / ( -2 * a * c)));
29 double C = Math.toDegrees(Math.acos((c * c - b * b - a * a)
30 / ( -2 * a * b)));
31
32 // Display results
33 System.out.println( "The three angles are " +
34 Math.round(A * 100 ) / 100 . 0 + " " +

compute sides

display result