*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**