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문제

모델 로켓으로 높이를 측정하는 방법중에 하나로 geodesic 이라는 방법이 있다. 두 관측자 A와 B가 기준선으로부터 100미터 떨어져있는 평평한 실험 구역위의 각 꼭지점에 서 있는다. 로켓이 발사되는 발사대는 관측자 A와 B로부터 같은 거리만큼 떨어져 있고 기준선으로부터 50미터 떨어져 있다. 각각의 관측자는 경위의(theodolite, 각도를 정밀하게 측정할수 있는 기계)또는 다른 장비를 갖고 있는데, 이 장치들은 떨어져 있는 물체의 앙각(대상을 보는 관측자의 시선이 수평면과 이루는 각)과 방위각(지평선에 따라 측정한 천체의 방향을 나타내는 각/여기서는 수평의 시선을 포함하는 수직면과 A, B를 지나는 선사이의 각도를 반시계방향으로 측정한 것)을 잰다. A의 장비는 발사대보다 HA미터만큼 위에 있고, B의 HB미터만큼 위에 있다. 로켓은 발사된 후, 가장 높게 올라간 이후에 낙하산을 펼치며 많은 양의 연기를 방출한다. 각각의 관측자들은 그들의 위치에서 로켓이 내보낸 연기의 앙각과 방위각을 측정한다.  만약 로켓이 최고로 다다른 위치가 기준선과는 다른 쪽이거나 A와 B가 판단할때 그 위치가 기준선과 수직인 선에서 벗어난 곳이라면 그 측정은 가치가 없다.

이 정보를 바탕으로 로켓의 높이는 다음과 같이 측정한다.

각각의 시선위에서, 다른 시선과 가장 가까운 지점을 시선위에서 찾아라. 이렇게 찾아진 두 점의 절반에 위치한 점이 로켓이 가장 최고 높이로 올라간 곳이라고 추정한다. 측정되어진 로켓은 발사대와 구한 점 사이의 수직거리다. 

HA(발사대 위에 있는 측정 장치 A의 거리)와 HB(발사대 위에 있는 측정 장치 B의 거리), 알파(왼쪽 관측자 A로 부터 측정된 앙각), 베타(오른쪽 관측자 B로부터 측정된 앙각), 감마(왼쪽 측정자 A로부터 측정된 방위각), 델타(오른쪽 측정자 B로부터 측정된 방위각)로부터 로켓의 높이를 측정하는 프로그램을 작성하시오.

입력

첫째 줄에 발사의 수 N(1 <= N <= 100), HA, HB가 주어진다. 이 숫자는 모두 실수이다. 둘째 줄부터 N개의 줄은 매번 발사할 때 마다 측정한 알파, 베타, 감마, 델타가 주어진다. 알파, 베타, 감마의 값은 0 ~ 90도 사이이고, 델타는 90 - 180도 사이이다.

출력

각각의 발사에 대해서, 로켓이 가장 높게 올라간 높이를 출력한다.

예제 입력 1

4 5.25 2.92
39.6 36.0 35.4 151.2
65.1 71.2 16.5 160.6
59.4 59.5 43.8 139.0
45.0 41.2 32.9 152.6

예제 출력 1

50
135
119
58
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A\uc758 \uc7a5\ube44\ub294 \ubc1c\uc0ac\ub300\ubcf4\ub2e4 HA\ubbf8\ud130\ub9cc\ud07c \uc704\uc5d0 \uc788\uace0, B\uc758 HB\ubbf8\ud130\ub9cc\ud07c \uc704\uc5d0 \uc788\ub2e4. \ub85c\ucf13\uc740 \ubc1c\uc0ac\ub41c \ud6c4, \uac00\uc7a5 \ub192\uac8c \uc62c\ub77c\uac04 \uc774\ud6c4\uc5d0 \ub099\ud558\uc0b0\uc744 \ud3bc\uce58\uba70 \ub9ce\uc740 \uc591\uc758 \uc5f0\uae30\ub97c \ubc29\ucd9c\ud55c\ub2e4. \uac01\uac01\uc758 \uad00\uce21\uc790\ub4e4\uc740 \uadf8\ub4e4\uc758 \uc704\uce58\uc5d0\uc11c \ub85c\ucf13\uc774 \ub0b4\ubcf4\ub0b8 \uc5f0\uae30\uc758 \uc559\uac01\uacfc \ubc29\uc704\uac01\uc744 \uce21\uc815\ud55c\ub2e4. &nbsp;\ub9cc\uc57d \ub85c\ucf13\uc774 \ucd5c\uace0\ub85c \ub2e4\ub2e4\ub978 \uc704\uce58\uac00 \uae30\uc900\uc120\uacfc\ub294 \ub2e4\ub978 \ucabd\uc774\uac70\ub098 A\uc640 B\uac00 \ud310\ub2e8\ud560\ub54c \uadf8 \uc704\uce58\uac00 \uae30\uc900\uc120\uacfc \uc218\uc9c1\uc778 \uc120\uc5d0\uc11c \ubc97\uc5b4\ub09c \uacf3\uc774\ub77c\uba74 \uadf8 \uce21\uc815\uc740 \uac00\uce58\uac00 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\uc774 \uc815\ubcf4\ub97c \ubc14\ud0d5\uc73c\ub85c \ub85c\ucf13\uc758 \ub192\uc774\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uce21\uc815\ud55c\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\uac01\uac01\uc758 \uc2dc\uc120\uc704\uc5d0\uc11c, \ub2e4\ub978 \uc2dc\uc120\uacfc \uac00\uc7a5 \uac00\uae4c\uc6b4 \uc9c0\uc810\uc744 \uc2dc\uc120\uc704\uc5d0\uc11c \ucc3e\uc544\ub77c. \uc774\ub807\uac8c \ucc3e\uc544\uc9c4 \ub450 \uc810\uc758 \uc808\ubc18\uc5d0 \uc704\uce58\ud55c \uc810\uc774 \ub85c\ucf13\uc774 \uac00\uc7a5 \ucd5c\uace0 \ub192\uc774\ub85c \uc62c\ub77c\uac04 \uacf3\uc774\ub77c\uace0 \ucd94\uc815\ud55c\ub2e4. \uce21\uc815\ub418\uc5b4\uc9c4 \ub85c\ucf13\uc740 \ubc1c\uc0ac\ub300\uc640 \uad6c\ud55c \uc810 \uc0ac\uc774\uc758 \uc218\uc9c1\uac70\ub9ac\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\r\n\tHA(\ubc1c\uc0ac\ub300 \uc704\uc5d0 \uc788\ub294 \uce21\uc815 \uc7a5\uce58 A\uc758 \uac70\ub9ac)\uc640 HB(\ubc1c\uc0ac\ub300 \uc704\uc5d0 \uc788\ub294 \uce21\uc815 \uc7a5\uce58 B\uc758 \uac70\ub9ac), \uc54c\ud30c(\uc67c\ucabd \uad00\uce21\uc790 A\ub85c \ubd80\ud130 \uce21\uc815\ub41c \uc559\uac01), \ubca0\ud0c0(\uc624\ub978\ucabd \uad00\uce21\uc790 B\ub85c\ubd80\ud130 \uce21\uc815\ub41c \uc559\uac01), \uac10\ub9c8(\uc67c\ucabd \uce21\uc815\uc790 A\ub85c\ubd80\ud130 \uce21\uc815\ub41c \ubc29\uc704\uac01), \ub378\ud0c0(\uc624\ub978\ucabd \uce21\uc815\uc790 B\ub85c\ubd80\ud130 \uce21\uc815\ub41c \ubc29\uc704\uac01)\ub85c\ubd80\ud130 \ub85c\ucf13\uc758 \ub192\uc774\ub97c \uce21\uc815\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n\r\n","input":"<p>\r\n\t\uccab\uc9f8 \uc904\uc5d0 \ubc1c\uc0ac\uc758 \uc218 N(1 &lt;= N &lt;= 100), HA, HB\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774 \uc22b\uc790\ub294 \ubaa8\ub450 \uc2e4\uc218\uc774\ub2e4. \ub458\uc9f8 \uc904\ubd80\ud130 N\uac1c\uc758 \uc904\uc740 \ub9e4\ubc88 \ubc1c\uc0ac\ud560 \ub54c \ub9c8\ub2e4 \uce21\uc815\ud55c \uc54c\ud30c, \ubca0\ud0c0, \uac10\ub9c8, \ub378\ud0c0\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc54c\ud30c, \ubca0\ud0c0, \uac10\ub9c8\uc758 \uac12\uc740 0 ~ 90\ub3c4 \uc0ac\uc774\uc774\uace0, \ub378\ud0c0\ub294 90 - 180\ub3c4 \uc0ac\uc774\uc774\ub2e4.<\/p>\r\n","output":"<p>\r\n\t\uac01\uac01\uc758 \ubc1c\uc0ac\uc5d0 \ub300\ud574\uc11c, \ub85c\ucf13\uc774 \uac00\uc7a5 \ub192\uac8c \uc62c\ub77c\uac04 \ub192\uc774\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2736","problem_lang":"1","title":"Model Rocket Height","description":"<p>One method used to determine the height achieved by a model rocket is the geodesic method. Two observers A and B are spaced 100 feet apart along a base line along one edge of the flat test field. The launch platform is equidistant from observers A and B and 50 feet from the base line. Each observer has a theodolite or some other device for measuring angle above the horizontal (elevation angle) of a distant object and the azimuth angle (the angle the vertical plane of the sight line makes with the line from A through B measured counter-clockwise). Each measuring device is on a stand. A&rsquo;s device is HA feet above the launch platform and B&rsquo;s device is HB feet above the launch platform. When a rocket is fired, near the top of its flight, it deploys a parachute and emits a puff of smoke. Each observer measures the elevation angle and azimuth angle of the puff of smoke from their location. If the peak location is on the wrong side of the baseline or outside the lines determined by A and B perpendicular to the base line, it is out of bounds and disqualified. From this information, the height of the rocket may be determined as follows:&nbsp;<\/p>\r\n\r\n<p>On each sight line, find the point on that sight line closest to the other sight line. The point halfway between these two points is assumed to be the location of the rocket at the top of its flight. The height achieved by the rocket is the vertical distance of this point above the launch platform.&nbsp;<\/p>\r\n\r\n<p>This problem is to write a program which, given the parameters HA (the distance of the measuring device A above the launch platform in feet), HB (the distance of the measuring device B above the launch platform in feet), &alpha; (the elevation angle of the rocket in degrees measured by the left observer A), &beta; (the elevation angle of the rocket in degrees observed by the right observer B), &gamma; (the azimuth angle in degrees measured by the left observer A) and &delta; (the azimuth angle in degrees measured by the right observer B), computes the height of the rocket above the launch platform in feet to the nearest foot.&nbsp;<\/p>\r\n","input":"<p>The first line of input contains the number of shots that follow N (1 &lt;= N &lt;= 100) and the parameters HA and HB in that order as decimal values (the values are separated by one or more spaces). These values would be measured once at the beginning of the day and remain fixed through all N rocket shots. Each succeeding line of input will contain the angles &alpha;, &beta;, &gamma; and &delta; in that order (measured in degrees) as decimal values. The angles &alpha;, &beta; and &gamma; will be strictly between 0 and 90 degrees and &delta; will be strictly between 90 degrees and 180 degrees.&nbsp;<\/p>\r\n","output":"<p>For each set of four angles (other than the end indicator), the output contains a line with the shot number, (1...N), a colon, a space and finally the height above the field in feet to the nearest foot with no leading spaces.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]