F4 Maths 3-D problems

👨🏻‍🏫 學術台數學

Anonymous

2010-03-17 2:25 am

The figure shows a rectangularblock of dimensions 8 cm x 8 cm x 7 cm.
AC = 11.3 cm, AG and CG = 10.6 cm respectively.
Angle AGC = 64.3 degree

Find the angle between the planes ACG and ABCD

Figure: http://img11.imageshack.us/img11/8167/maths18.jpg

更新1:

deathnotesimonxdd: Where is K?

回答 (2)

匿名

2010-03-17 3:44 am

✔ 最佳答案

Extand G to meet AC at K, such that KB perpendicular to BG
Angle required is <BKG,
AC=√(2*8^2)
AC=8√2 cm
BK*AC = 8*8
BK = 8/√2 cm
tan<BKE = 7/(8/√2)
<BKE = 51.1deg (corr. to 3 sig. fig.)
Hence, the angle between the planes ACG and ABCD is 51.1 deg

2010-03-16 21:40:01 補充：
Extand G to meet AC at K, such that KB perpendicular to BG

2010-03-16 21:42:19 補充：
http://img267.imageshack.us/i/maths18.jpg/

參考: Hope can help you^^”

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用戶7639

2010-03-17 3:39 am

51.0度~~~~~~~~~~~

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收錄日期: 2021-04-23 20:40:35
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