緊急架!!!中四maths!三角學.

用餘弦定理 :
b:c=1:3 -----> c = 3b
cosA = (b^2 + c^2 - a) / 2bc
cos35° = (b^2 + (3b)^2 - 25) / [2b(3b)]
(cos35°)(6b^2) = 10b^2 - 25
(10 - 6cos35°)b^2 = 25
b = 2.21728
c = 3 * 2.21728 = 6.65184
三角形ABC面積 = (1/2)(sin35)bc
= (1/2)(sin35)(2.21728)(6.65184)
= 4.23 cm^2


2010-06-07 22:50:08 補充：
更正 , 錯式 :

用餘弦定理 :

b:c=1:3 -----> c = 3b

cosA = (b^2 + c^2 - a^2) / 2bc

cos35° = (b^2 + (3b)^2 - 25^2) / [2b(3b)]

(cos35°)(6b^2) = 10b^2 - 625

(10 - 6cos35°)b^2 = 625

b = 11.08641

c = 11.08641*3 = 33.25922

三角形ABC面積 = (1/2)(sin35°)bc

= (1/2)(sin35°)(11.08641)(33.25922)

= 105.746 cm^2

2010-06-07 22:54:20 補充：
更正 , 背錯式 :

用餘弦定理 :

b:c=1:3 -----> c = 3b

cosA = (b^2 + c^2 - a^2) / 2bc

cos35° = (b^2 + (3b)^2 - 25^2) / [2b(3b)]

(cos35°)(6b^2) = 10b^2 - 625

(10 - 6cos35°)b^2 = 625

b = 11.08641

c = 11.08641*3 = 33.25922

三角形ABC面積 = (1/2)(sin35°)bc

= (1/2)(sin35°)(11.08641)(33.25922)

= 105.746 cm^2