Question

hua

想問這題🙏🏻

例題5
tan
平方關係與餘角關係
x
10
配合課本P.182隨堂練習
如右圖,AB⊥BC,DC⊥BC,AE、DE分別為∠DAB、∠ADC的角
平分線,且AB=1,AD=6,試求 CD 長。
| √6
A
a
a
(A)√6-√3
(B)√6-√√2
(C)~6-1
1
A
(D)V2
(E)√3
[黎明中學]
B
E
C

Answer 1

qn

α + β = 90°

AE = 1/cosα = √6 cosα
→ cos²α = 1/√6

CD = DE·cosβ
= (√6 cosβ)·cosβ
= √6 cos²β
= √6 sin²α
= √6 (1 - cos²α)
= √6 - √6 cos²α
= √6 - √6 · (1/√6)
= √6 - 1