# C Program to find hypotenuse without math.h

Write a C program to find hypotenuse of a right-angled triangle without using math.h.

Let be the perpendicular and be the base of a right-angled triangle. The hypotenuse, is given by

We can easily find the hypotenuse using the above formula but the catch is we cannot use math.h. Therefore, we cannot use sqrt() to calculate the square root.

We will implement our own sqrt() function. We can do it using Newton’s method or Binary Search (both methods are very similar). In this post, we will use binary search to find the square root of a number.

## Program

#include<stdio.h>
#include<string.h>

// function to calculate square root of n
// using binary search
double sqrt(double n){

double start,end,mid;
// the square root of n must lie between 0 and n
start = 0, end = n;
// in each iteration, we compare mid with n
// and modify start and end such that they converge
// closer and closer to square root of n
while((end - start)>=0.000001){
mid = (start + end)/2;
if(mid*mid < n)
start = mid;
if(mid*mid >= n)
end = mid;
}
return mid;

}

int main() {

double H,B,P;
printf("Enter Base of the Triangle: ");
scanf("%lf", &B);
printf("Enter Height/Perpendicular of the Triangle: ");
scanf("%lf", &P);
H = sqrt(B*B + P*P);
printf("Hypotenuse of Triangle: %lf", H);

}

Output