Re: [幾何] 角度問題

[Honor1984 (希望願望成真)]

※ 引述《a5718090610 (Linear)》之銘言：
: When lengths of AB, BC and CD are equal, find the angle ∠BCD
: https://www.dropbox.com/s/h24ezrur327wjo0/%E6%9C%AA%E5%91%BD%E5%90%8D.png
: 這個是圖~
: 不好意思~小弟解了1H都解不出來~請問有人可以幫我解出來嗎? 謝謝~

設AB = a

∠CBD = 90 - x/2

以下角度均用度數

BD = 2asin(x/2)

2asin(x/2)          a
----------  =  -------------
  sin(54)      sin(108 - x/2)

=> 2sin(x/2)[sin(108)cos(x/2) - cos(108)sin(x/2)] = sin(54)

=> sin(108)sin(x) + cos(108)cos(x) = sin(54) + cos(108)

=> cos(108 - x) = sin(54) + cos(108)

=> x = 108 - arccos(sin(54) + cos(108)) 度數

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→ Honor1984   := 108 - 60 = 48度