【題目敘述】https://vjudge.net/problem/UVA-10221
【解題想法】
- Degrees (°), minutes (‘), seconds (“)
- 1° = 60′
- 1′ = 60″
- 角度 degree (deg) vs. 弧度 radius (rad)
- 一個完整的圓的弧度：2 * PI
- rad = deg / 180 * PI
- cos (90°) = 0 -> acos(0) = PI / 2 -> PI = 2 * acos(0)
- 一個半徑為 R 的圓，圓周長為 2 * PI * R，當兩顆衛星之間的夾角「角度」為 a°（a 大於 180 時，a -> 360 – a）
- 弧長 arc = 2 * PI * R * a / 360
- 弦長 chord = 2* R * cos((90 – a / 2) / 180 * PI)
#include <iostream>
#include <iomanip>
#include <cmath>
using namespace std;
#define PI acos(0.0)*2.0
int main() {
double r, s, a;
string unit;
double chord, arc;
r = 6440.0;
while (cin >> s >> a >> unit){
if (unit == "min") a /= 60.0;
if (a > 180.0) a = 360.0 - a;
chord = (r+s) * cos((90.0 - a/2.0)/ 180.0 * PI) * 2.0;
arc = 2.0 * PI * (r+s) * a / 360.0;
cout << fixed << setprecision(6) << arc << " " << chord << "\n";
}
return 0;
}