F4 Maths 3-D problems Zzz

2010-03-20 9:35 pm

In the figure, a tent ABCDEF is in the shape of a triangular prism with
angle DEC = 65 degree. ABCD and ADEF are two identical rectangular
planes of dimensions 3 m x 2 m. Find

a) the angle between BD and the plane BCEF

b) the angle between BD and DE

Figure: http://img39.imageshack.us/img39/8409/maths25.jpg

回答 (1)

用戶2053

2010-03-20 10:15 pm

✔ 最佳答案

圖片參考：http://img39.imageshack.us/img39/8409/maths25.jpg

a)Let the required angle be x , m be the mid point of CE :

sin x = DM / BD......*

DM / DE = DM / 2 = sin65°

DM = 2sin65°

BD = √(2^2 + 3^2) = √13 , sub to * :

sin x = 2sin65° / √13

x = 30.18072°

b)

(CE/2) / DE = CE/4 = cos65°

CE = 4cos65°

BE^2 = 3^2 + (4cos65°)^2

The required angle = ㄥBDE ,

cos ㄥBDE = (BD^2 + DE^2 - BE^2) / (2 BD DE)

cos ㄥBDE = [13 + 2^2 - (3^2 + (4cos65°)^2)] / [2 (√13) (2)]

cos ㄥBDE = 0.35655

ㄥBDE = 69.11°

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