maths_16

(a)
DADK 中：
tan32o = (a cm)/AK 及 sin32o = (a cm)/AD
AK = a/tan32o cm 及 AD = a/sin32o cm

DABD 中：
∠ABD = 90o - 56o = 34o
tan∠ABD = AD/AB 及 sin∠ABD = AD/BD
tan34o = (a/sin32o cm)/AB 及 sin34o = (a/sin32o cm)/BD
AB = a/sin32otan34o cm 及 BD = a/sin32osin34o cm

DBDK 中：
sin∠DBK = a/(a/sin32osin34o)
sin∠DBK = sin32osin34o
BD 的傾角 ∠DBK = 17.24o


(b)
DABK 中：
tan∠ABK = AK/AB
tan∠ABK = (a/tan 32o)/(a/sin32otan34o)
tan∠ABK = sin32otan34o/tan32o
∠ABK = 29.77o
90o - 29.77 = 60.23o
由 B 測得 D 的方位角 = N 60.23o W
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