找出我们可以倾斜瓶子而不洒水的最大角度

给定一个长方体形状的水瓶，其底边是边长为 x cm，高为 y cm 的正方形，任务是找到我们可以倾斜瓶子而不会洒出任何水的最大角度，当 z 立方厘米时将水倒入瓶中，并围绕底座的一侧逐渐倾斜瓶。

例子：

Input: x = 2, y = 2, z = 4
Output: 45.00000
Explanation:
This bottle has a cubic shape,
and it is half-full. 
The water gets split when we tilt
the bottle more than 45 degrees.

Input: x = 12, y = 21, z = 10
Output: 89.78346

方法：
首先，我们需要知道水面始终与地面平行。因此，如果瓶子倾斜，水将保持与地面平行。
这里我们有两种情况：-

1. 当水量小于瓶子总体积的一半时，则考虑瓶子内部的水形成的右下三角形，并借助切线求逆计算所需的角度。
2. 当水量大于等于瓶子的总体积时，我们考虑瓶子内部的空间形成的右上三角形。现在我们可以轻松计算角度。

下面是上述方法的实现：

C++

// C++ program to find the maximum angle
// at which we can tilt the bottle
// without spilling any water
 
#include 
using namespace std;
 
float find_angle(int x, int y, int z)
{
 
    // Now we have the volume
    // of rectangular prism a*a*b
    int volume = x * x * y;
 
    float ans = 0;
 
    // Now we have 2 cases!
    if (z < volume / 2) {
 
        float d = (x * y * y) / (2.0 * z);
 
        // Taking the tangent inverse of value d
        // As we want to take out the required angle
        ans = atan(d);
    }
    else {
 
        z = volume - z;
        float d = (2 * z) / (float)(x * x * x);
 
        // Taking the tangent inverse of value d
        // As we want to take out the required angle
        ans = atan(d);
    }
 
    // As of now the angle is in radian.
    // So we have to convert it in degree.
    ans = (ans * 180) / 3.14159265;
 
    return ans;
}
 
int main()
{
    // Enter the Base square side length
    int x = 12;
 
    // Enter the Height of rectangular prism
    int y = 21;
 
    // Enter the Base square side length
    int z = 10;
 
    cout << find_angle(x, y, z) << endl;
}

Java

// Java program to find the maximum angle
// at which we can tilt the bottle
// without spilling any water
class GFG
{
    static float find_angle(int x,
                     int y, int z)
    {
 
        // Now we have the volume
        // of rectangular prism a*a*b
        int volume = x * x * y;
 
        float ans = 0;
 
        // Now we have 2 cases!
        if (z < volume / 2)
        {
            float d = (float) ((x * y * y) / (2.0 * z));
 
            // Taking the tangent inverse of value d
            // As we want to take out the required angle
            ans = (float) Math.atan(d);
        }
        else
        {
            z = volume - z;
            float d = (2 * z) / (float) (x * x * x);
 
            // Taking the tangent inverse of value d
            // As we want to take out the required angle
            ans = (float) Math.atan(d);
        }
 
        // As of now the angle is in radian.
        // So we have to convert it in degree.
        ans = (float) ((ans * 180) / 3.14159265);
 
        return ans;
    }
 
    // Driver Code
    public static void main(String[] args)
    {
        // Enter the Base square side length
        int x = 12;
 
        // Enter the Height of rectangular prism
        int y = 21;
 
        // Enter the Base square side length
        int z = 10;
 
        System.out.print(find_angle(x, y, z) + "\n");
    }
}
 
// This code is contributed by PrinciRaj1992

Python3

# Python3 program to find the maximum angle
# at which we can tilt the bottle
# without spilling any water
from math import *
 
def find_angle(x, y, z) :
 
    # Now we have the volume
    # of rectangular prism a*a*b
    volume = x * x * y;
 
    ans = 0;
 
    # Now we have 2 cases!
    if (z < volume // 2) :
 
        d = (x * y * y) / (2.0 * z);
 
        # Taking the tangent inverse of value d
        # As we want to take out the required angle
        ans = atan(d);
 
    else :
 
        z = volume - z;
        d = (2 * z) / (float)(x * x * x);
 
        # Taking the tangent inverse of value d
        # As we want to take out the required angle
        ans = atan(d);
     
    # As of now the angle is in radian.
    # So we have to convert it in degree.
    ans = (ans * 180) / 3.14159265;
 
    return round(ans, 4);
 
# Driver Code
if __name__ == "__main__" :
 
    # Enter the Base square side length
    x = 12;
 
    # Enter the Height of rectangular prism
    y = 21;
 
    # Enter the Base square side length
    z = 10;
 
    print(find_angle(x, y, z));
 
# This code is contributed by AnkitRai01

C#

// C# program to find the maximum angle
// at which we can tilt the bottle
// without spilling any water
using System;
 
class GFG
{
    static float find_angle(int x,
                     int y, int z)
    {
 
        // Now we have the volume
        // of rectangular prism a*a*b
        int volume = x * x * y;
 
        float ans = 0;
 
        // Now we have 2 cases!
        if (z < volume / 2)
        {
            float d = (float) ((x * y * y) / (2.0 * z));
 
            // Taking the tangent inverse of value d
            // As we want to take out the required angle
            ans = (float) Math.Atan(d);
        }
        else
        {
            z = volume - z;
            float d = (2 * z) / (float) (x * x * x);
 
            // Taking the tangent inverse of value d
            // As we want to take out the required angle
            ans = (float) Math.Atan(d);
        }
 
        // As of now the angle is in radian.
        // So we have to convert it in degree.
        ans = (float) ((ans * 180) / 3.14159265);
 
        return ans;
    }
 
    // Driver Code
    public static void Main(String[] args)
    {
        // Enter the Base square side length
        int x = 12;
 
        // Enter the Height of rectangular prism
        int y = 21;
 
        // Enter the Base square side length
        int z = 10;
 
        Console.Write(find_angle(x, y, z) + "\n");
    }
}
 
// This code is contributed by Rajput-Ji

Javascript

// javascript program to find the maximum angle
// at which we can tilt the bottle
// without spilling any water
 
    function find_angle(x , y , z) {
 
        // Now we have the volume
        // of rectangular prism a*a*b
        var volume = x * x * y;
 
        var ans = 0;
 
        // Now we have 2 cases!
        if (z < volume / 2) {
            var d =  ((x * y * y) / (2.0 * z));
 
            // Taking the tangent inverse of value d
            // As we want to take out the required angle
            ans =  Math.atan(d);
        } else {
            z = volume - z;
            var d = (2 * z) /  (x * x * x);
 
            // Taking the tangent inverse of value d
            // As we want to take out the required angle
            ans =  Math.atan(d);
        }
 
        // As of now the angle is in radian.
        // So we have to convert it in degree.
        ans =  ((ans * 180) / 3.14159265);
 
        return ans;
    }
 
    // Driver Code
     
        // Enter the Base square side length
        var x = 12;
 
        // Enter the Height of rectangular prism
        var y = 21;
 
        // Enter the Base square side length
        var z = 10;
 
        document.write(find_angle(x, y, z).toFixed(4) + "\n");
 
// This code is contributed by todaysgaurav

输出：

89.7835

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