Question

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如右圖,△ABC的三邊長AB=5、BC=6、CA=7。若四邊形ABDE、ACFG皆為正方
形,試求EG 的值。
9x4×3×2
3
2 x 3
6AGE
-
5x7 sino = 656
2
0203 (2)
Onie (1)
G
E
3
5
D
B b
C
45
656

Answer 1

qn

cos∠BAC = (5²+7²-6²)/(2·5·7)
= 19/35
cos∠EAG = cos(180°-∠BAC)
= -cos∠BAC
= - 19/35

EG² = 5² + 7² - 2·5·7·(-19/35)
= 25 + 49 + 38
= 112
EG = √112 = 4√7