急!!!教我1題數..THx.

AD是∠BAC的角平分線
∴∠BAD=∠CAD=∠BAC÷2
∴∠BAD=∠CAD=53.130°÷2 (5位有效數字比較好些)
∴∠BAD=∠CAD=26.565°
ΔBAD + ΔCAD = ΔABC
0.5(10 cm)AD sin 26.565° + 0.5(8 cm)AD sin 26.565°= 32 cm²
9 AD sin 26.565°= 32 cm
AD = 7.95 cm (3位有效數字)

2007-08-30 23:45:49 補充：
你試試圖畫出來(真的用鉛筆、直尺)你會發現AD的長度真的是約8cm用這個方法,對check數真的很有效,你不妨試試

Area of ABC = 1/2 * 10 * 8 sin∠BAC
∠BAC= 53.13
∠BAD= 26.56505 (∠bisector)

Using Cosine formula,
BC^2= 10^2 + 8^2 - 2(10)(8)cos∠BAC
BC= √68

Using Cosine formula again
8^2 = 68 + 10^2 - 2(√68)(10)cos∠ABC
∠ABC= 50.90614
∠ADB=180-50.90614-26.5605 (∠sum of triangle)
=102.5288077
using sin formula
AD/ sin ∠ABD = 10/ sin ∠ADB
AD=7.95 (corr.to 3 sig. fig.)

i don't know the answer is correct or not... may be you can calculate once more by yourself to check it