找到我们可以倾斜瓶子而不溅出任何水的最大角度
原文:https://www . geeksforgeeks . org/find-我们可以倾斜瓶子而不会溅出任何水的最大角度/
给定一个底部为边 x cm、高 y cm 的正方形的矩形棱柱形状的水瓶，任务是找到当 z 立方 cm 的水倒入瓶中时，我们可以倾斜瓶子而不溅出任何水的最大角度，并围绕底部的一边逐渐倾斜瓶子。
示例:
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
进场: 首先，我们需要知道水面始终与地面平行。所以如果瓶子倾斜，水保持与地面平行。 这里有两种情况:-
- 当水少于瓶子总体积的一半时，那么我们考虑瓶子内部水形成的右下三角形，并借助切线反算出所需的角度。
- 当水大于或等于瓶子的总体积时，那么我们考虑瓶子内部的空白空间形成的右上三角形。现在我们可以很容易地计算角度。
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 <bits/stdc++.h>
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 语言(一种计算机语言，尤用于创建网站)
// 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
Python 3
# 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
java 描述语言
<script>
// 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
</script>
Output:
89.7835
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