C++ :: Testing Cos - Why Angle Is Not 45 Degrees

I developed this simple sample program to test cos():

Code:
#include <cmath>
#include <iostream>
using namespace std;
int main() {
const float radiansToDegrees = 180.0f / 3.141592653589793f;
float c = sqrt(2.0f);
float a = 1;
float angleRadians = cos(a/c);
float angle = radiansToDegrees*angleRadians;
}

I expected angle to be 45 exactly, but it's value is: angle = 43.558804

Why is the angle not 45 degrees? What did I do wrong?