解三角學的問題,~急~

2009-11-20 9:03 pm
1,有一塔在正午時分,陽光與地平線成30度角。這時,
地面上的塔的影子長109m。己知塔的傾斜角為5.5度,若此塔
不傾斜,求塔高。(答案準確至最接近的m。)

回答 (2)

2009-11-20 11:14 pm
✔ 最佳答案

圖片參考:http://i320.photobucket.com/albums/nn347/old-master/20091120_1.jpg?t=1258701191

http://i320.photobucket.com/albums/nn347/old-master/20091120_1.jpg?t=1258701191

2009-11-20 15:57:22 補充:
另一方法是作AH垂直於AC,垂足為H。

ΔBCH中:
∠CBH = 5.5º
BH = BCcos5.5º
HC = BCsin5.5o

ΔABH中:
AH = BH/tan30º = BCcos5.5º/tan30º

AH + HC = 109 m
BCcos5.5º/tan30º + BCsin5.5o = 109 m
BC = 109/[(cos5.5º/tan30º) + sin5.5o] m = 60 m
不傾斜時,塔高 = 60 m
2009-11-20 10:03 pm

109tan(30度)sec(5.5度)
=63(m)

2009-11-20 14:14:30 補充:
另一解

設塔高x
[xsin(5.5 度)+109]tan(30度)=xcos(5.5度)
109tan(30度)=x[cos(5.5度)-sin(5.5度)]
x=69.95約=70(m)

2009-11-20 14:17:33 補充:
另一解
[xsin(5.5度)+109]tan(30度)=xcos(5.5度)
109tan(30度)=x[cos(5.5度)- sin(5.5度)]
x=69.95約=70(m)

2009-11-20 14:17:50 補充:
另一解
[xsin(5.5度)+109]tan(30度)=xcos(5.5度)
109tan(30度)=x[cos(5.5度)- sin(5.5度)]
x=69.95約=70(m)


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