Atcoder abc 168 C

C - : (Colon)

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Time Limit: 2 sec / Memory Limit: 1024 MB

Score: 300300 points

Problem Statement

Consider an analog clock whose hour and minute hands are AA and BB centimeters long, respectively.

An endpoint of the hour hand and an endpoint of the minute hand are fixed at the same point, around which each hand rotates clockwise at constant angular velocity. It takes the hour and minute hands 1212 hours and 11 hour to make one full rotation, respectively.

At 00 o'clock, the two hands overlap each other. HH hours and MM minutes later, what is the distance in centimeters between the unfixed endpoints of the hands?

Constraints

• All values in input are integers.
• 1≤A,B≤10001≤A,B≤1000
• 0≤H≤110≤H≤11
• 0≤M≤590≤M≤59

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Input

Input is given from Standard Input in the following format:

AA BB HH MM

Output

Print the answer without units. Your output will be accepted when its absolute or relative error from the correct value is at most 10−910−9.

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Sample Input 1 Copy

Copy

3 4 9 0

Sample Output 1 Copy

Copy

5.00000000000000000000

The two hands will be in the positions shown in the figure below, so the answer is 55 centimeters.

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Sample Input 2 Copy

Copy

3 4 10 40

Sample Output 2 Copy

Copy

4.56425719433005567605

The two hands will be in the positions shown in the figure below. Note that each hand always rotates at constant angular velocity.

思路：余弦定理。

#include<iostream>
#include<cmath>
#define dou double

using namespace std;

const dou pie = acos(-1.0);

int main()
{
	dou a,b,h,m;
	cin>>a>>b>>h>>m;
	double x = h * 60 + m;
	x /= 720;
	x *= 2 * pie;
	double y = m / 60 * 2 * pie;
	double z = abs(x - y);
	dou ans = sqrt(a*a + b*b -2*a*b*cos(z));
	printf("%.9lf",ans);
	return 0;
}