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標題:
maths F.3 --urgent
發問:
A helicopter is flying 300m above the sea. The pilot observes that the angles of depression of two ships, which are both due East, are 28 and 58 respectively. Find the distance between the two ships. 請 draw 個diagram 出來圖解. Thanks
最佳解答:
乜點都無好難計 設helicopter既位置叫 A helicopter既位置垂直點落去個海面個點叫B ship a 叫C ship b 叫D AB垂直BC BCD為一直線 (其實我係唔想打英文 自己轉翻啦) AB=300 angleBAC = 28 angleBAD=58 tan28=BC/AB 300tan28=BC tan58=BD/AB 300tan58=BD BD-BC=CD 300tan58-300tan28=CD CD=320.5875 The distance between the two ships are 321m diagram 一陣補翻 2008-05-18 17:28:09 補充： http://www.alfa2.info/0611/helicopter&ships.GIF 圖片連結 畫得樣衰 希望諒解
其他解答:
http://hk.myblog.yahoo.com/aludramak/article?new=1&mid=2 Please look at the link above for the picture. Assume point O is the point directly from the helicopter. We need to find out distance between A (ship A) and B (ship B). So it will be OB - OA Due to the reason of ALT angle, we know that angle HBO = 28 degree and HAO = 58 degree tan 58 = 300 / OA OA = 300 / tan 58 OA = 187.46080557 = 187.461 (to 3 decimal places) tan 28 = 300 / OB OB = 300 / tan 28 OB = 564.2179396 = 564.218 (to 3 decimal places) Threfore: AB = OA - OB = 564.218 - 187.461 = 376.757m NOTE: The definition of angle of depression from the other answer is incorrect... 2008-05-19 04:29:20 補充： Sorry, it should be: Threfore: AB = OB - OA = 564.218 - 187.461 = 376.757m
maths F.3 --urgent
發問:
A helicopter is flying 300m above the sea. The pilot observes that the angles of depression of two ships, which are both due East, are 28 and 58 respectively. Find the distance between the two ships. 請 draw 個diagram 出來圖解. Thanks
最佳解答:
乜點都無好難計 設helicopter既位置叫 A helicopter既位置垂直點落去個海面個點叫B ship a 叫C ship b 叫D AB垂直BC BCD為一直線 (其實我係唔想打英文 自己轉翻啦) AB=300 angleBAC = 28 angleBAD=58 tan28=BC/AB 300tan28=BC tan58=BD/AB 300tan58=BD BD-BC=CD 300tan58-300tan28=CD CD=320.5875 The distance between the two ships are 321m diagram 一陣補翻 2008-05-18 17:28:09 補充： http://www.alfa2.info/0611/helicopter&ships.GIF 圖片連結 畫得樣衰 希望諒解
其他解答:
http://hk.myblog.yahoo.com/aludramak/article?new=1&mid=2 Please look at the link above for the picture. Assume point O is the point directly from the helicopter. We need to find out distance between A (ship A) and B (ship B). So it will be OB - OA Due to the reason of ALT angle, we know that angle HBO = 28 degree and HAO = 58 degree tan 58 = 300 / OA OA = 300 / tan 58 OA = 187.46080557 = 187.461 (to 3 decimal places) tan 28 = 300 / OB OB = 300 / tan 28 OB = 564.2179396 = 564.218 (to 3 decimal places) Threfore: AB = OA - OB = 564.218 - 187.461 = 376.757m NOTE: The definition of angle of depression from the other answer is incorrect... 2008-05-19 04:29:20 補充： Sorry, it should be: Threfore: AB = OB - OA = 564.218 - 187.461 = 376.757m
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