maths F.3 --urgent

2008-05-18 10:30 pm
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

回答 (2)

2008-05-19 1:24 am
✔ 最佳答案
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
2008-05-19 12:27 pm
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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