三角形ABC , AB=1, AC=2 邊BC 和由A點連到BC的中線等長
問BC長?
A(1+ 根號2)/2
B (1+ 根號3)/2
C 根號2
D 3/2
E 根號3
Original Question
1. In triangle ABC, AB = 1 and AC = 2. Side BC and the median from A to BC have the same length. What is BC?
a) (1 + root2)/2b) (1 + root3)/2c) root2d) 3/2 e) root3
三角形數學問題!!!
2006-12-11 10:18 pm
回答 (1)
2006-12-11 11:32 pm
✔ 最佳答案
令由A點連到BC的中線和BC相交於D點且∠ADB = θ1，∠ADC = θ2
令BD=DC=X，則AD=2X
對△ADB來說
cos(θ1) = [X^2+(2X)^2 - 1^2] / 4X^2.......(1)
對△ADC來說
cos(θ2) = [X^2+(2X)^2 - 2^2] / 4X^2.......(2)
∵θ1+θ2 = 180(度)
∴cos(θ1) = - cos(θ2)........(3)
由(1)(2)(3)可得[X^2+(2X)^2 - 1^2] = - [X^2+(2X)^2 - 2^2]
解得 X = √2 / 2
BC的長 = 2X = √2
所以答案是(C)
參考: 我自己
收錄日期: 2021-04-26 15:14:33
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20061211000015KK05074