F.4 Maths Questions

Area ABC = bcsinA / 2 --------- (1)

by sine law:
sinA / a = sin B/b = sin C /c

therefore:
b = a sin B/ sinA ------ (2)
c = a sin C/ sinA ------ (3)

A + B + C =180
A = 180 - B + C -------(4)

sub (2) & (3) into (1)
Area ABC = a² sinB sinC /2 sin²A
Area ABC = a² sinB sinC /2 sin²(180- B - C)
= a² sinB sinC /2 sin²(B + C)




2011-05-03 14:39:36 補充：
更正一下

sub (2) & (3) into (1)
Area ABC = a² sinA sinB sinC /2 sin²A
Area ABC = a² sinB sinC /2 sin(180- B - C)
= a² sinB sinC /2 sin(B + C)