For this question, you will write several methods for your own Math class. These should all be inside a class called Hypotenuse. Write these methods on the provided paper. If you run out of space, more paper will be provided. Make sure that your name and student number are written on the extra paper.
Write a method called absVal. This method takes as input a real number and outputs the absolute value of that number. For example absVal(3.5) should return 3.5, absVal(-4) should return 4, and absVal(0) should return 0. You may NOT use any library methods to help for this question.
Write a method called power. This method takes as input a real number, x, and an integer number, y. It outputs the real number to the power of the integer number, xy. You can assume that the exponent (the integer, y) is non-negative (but it might be 0). You may NOT use any library methods to help for this question.
Write a method called squareRoot. This method takes as input a real number, y, and outputs its square root, vy. You will do this using the Babylonian method described in detail below. You may NOT use any library methods to help for this question.
The Babylonian method for approximating the square root of a number works by making successive "guesses" (denoted by x0 , x1 , ...xk below) which get closer and closer to the actual value. Once the difference between successive guesses is very small, the method stops and the final guess is considered to be the answer.
- The first guess :x0 = y 2
- Subsequent guesses: Repeat xk+1 = 1 (xk + y ) 2 xk
- Stop when the difference between successive values of xk and xk+1 is less than 0.1. - The answer is the last value of xk+1.
For this question, if the method input is negative, you should take the absolute value of the input before computing the square root. Do this using the absVal method you wrote in part 1.
Inside of the class Hypotenuse, write a main method. Your method will ask the user for two floating point numbers as input and obtain them using a Scanner type variable.
These numbers correspond to the base and the height of a right angle triangle. It then calculates and prints the length of the hypotenuse. Recall that c2 = a2 + b2 where c is the length of the hypotenuse and a and b are the lengths of the base and the height. Use the power and squareRoot methods that you wrote previously to do this.