Question

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向各位大神請教13、14題的解法！！十分感謝！！！

為以原品為圓的單位圆
已知 tan
5
12
求PQ之長為1号
12
0
O
PQ = PO = 12 = 5 = 1 / 2 = 1
13. 如圖,△ABC中,∠A=90°,D在AC上,DEBC,
若AD=2DC,AB=4DE,求sinB 的值為
4%
3
4
B
E
ACDE~DABC
=> 2CDE = 2B
14.右圖為一單位圓半徑為1),4T為切線,PQx軸,PR┻y軸,
3
14
AT: =
,求矩形OQPR的周長為
R
O
QA
D
D

三角函數

Answer 1

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13.
三角形ABC和三角形EDC相似(AA)
AB : ED = AC : EC = 4 : 1
EC = AC/4
sinB = sin角CDE = EC/CD = (AC/4)/(AC/3) = 3/4

14.
令角POA為θ
AT = tanθ = 3/4
PQ = sinθ = 3/5
OQ = cosθ = 4/5
所求 = 2(3/5 + 4/5) = 14/5

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感謝~~~~我都弄懂了~~~