Show that the area of 三角形ABC= (a^2 SinBSinC) ÷ [2Sin(B+C)]
ps. a^2 是指 a 的二次方
中四第11課 嘅三角形面積個課，
只要給我一些提示就可以，如果識得就幫幫我!
Thanks..............! 本人感激不盡(哭)
數學問題教教我
2012-09-23 11:03 pm
回答 (1)
2012-09-23 11:43 pm
✔ 最佳答案
Bysine law, in ΔABC :b/sinB = a/sinA
b sinA = a sinB ...... [1]
The sum of interior angles of ΔABC :
A + B + C = 180°
180° - A = B + C
sin(180° - A) = sin(B + C)
sinA = sin(B + C) ...... [2]
Area of ΔABC
= [a b sinC] ÷ 2
= [a b sinC sinA] ÷ [2 sinA]
= [a (b sinA) sinC] ÷ [2 sinA]
= [a (a sinB) sinC] ÷ [2 sinA] ...... from [1]
= [a² sinB sinC] ÷ [2 sin(B + C)] ...... from [2]
參考: sioieng
收錄日期: 2021-04-13 18:59:13
原文連結 [永久失效]:
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