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Bovier-Lapierre - Traité élémentaire de trigonométrie rectiligne 1868.djvu/75
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Calcul de
φ
{\displaystyle \varphi }
.
log
tang
φ
=
log
b
−
log
a
{\displaystyle \log \operatorname {tang} \varphi =\log b-\log a}
log
b
=
1,802
40
{\displaystyle \ \;\log b=1{,}80240}
log
a
=
2,123
59
{\displaystyle \ \;\log a=2{,}12359}
log
tang
φ
=
1
¯
,
67881
{\displaystyle \log \operatorname {tang} \varphi ={\overline {1}}{,}67881\quad \ \ }
φ
=
25
∘
30
′
58
′
′
{\displaystyle \qquad \ \ \ \varphi =25^{\circ }30^{\prime }58^{\prime \prime }}
Calcul de
A
et de
B
dans le triangle
ABC.
log
tang
A
−
B
2
=
log
tang
A
+
B
2
+
log
tang
(
45
∘
−
φ
)
{\displaystyle \log \operatorname {tang} {\frac {\mathrm {A-B} }{2}}=\log \operatorname {tang} {\frac {\mathrm {A+B} }{2}}+\log \operatorname {tang} (45^{\circ }-\varphi )}
A
+
B
2
=
90
∘
−
A
C
B
2
=
69
∘
16
′
32
′
′
{\displaystyle {\frac {\mathrm {A+B} }{2}}=90^{\circ }-{\frac {\mathrm {ACB} }{2}}=69^{\circ }16^{\prime }32^{\prime \prime }}
45
∘
−
φ
=
19
∘
29
′
2
′
′
{\displaystyle 45^{\circ }-\varphi =19^{\circ }29^{\prime }2^{\prime \prime }}
log
tang
A
+
B
2
=
0,422
10
{\displaystyle \log \operatorname {tang} {\frac {\mathrm {A+B} }{2}}=0{,}42210}
log
tang
(
45
∘
−
φ
)
=
1
¯
,
54877
{\displaystyle \log \operatorname {tang} (45^{\circ }-\varphi )={\overline {1}}{,}54877}
log
tang
A
−
B
2
=
1
¯
,
97087
{\displaystyle \log \operatorname {tang} {\frac {\mathrm {A-B} }{2}}={\overline {1}}{,}97087}
A
−
B
2
=
43
∘
4
′
48
′
′
{\displaystyle \qquad \qquad {\frac {\mathrm {A-B} }{2}}=43^{\circ }4^{\prime }48^{\prime \prime }}
A
=
112
∘
21
′
20
′
′
{\displaystyle \qquad \qquad \qquad \quad \ \ \mathrm {A} =112^{\circ }21^{\prime }20^{\prime \prime }}
B
=
26
∘
11
′
44
′
′
{\displaystyle \qquad \qquad \qquad \ \ \ \ \;\mathrm {B} =\ \ 26^{\circ }11^{\prime }44^{\prime \prime }}
Calcul de
c
dans le triangle
ABC.
log
c
=
log
a
+
log
sin
C
−
log
sin
A
{\displaystyle \log c=\log a+\log \sin \mathrm {C} -\log \sin \mathrm {A} }
log
a
=
2,123
59
log
sin
C
=
1
¯
,
82083
−
log
sin
A
=
0,033
93
{\displaystyle {\begin{aligned}\log a&=2{,}12359\\\log \sin \mathrm {C} &={\overline {1}}{,}82083\\-\log \sin \mathrm {A} &=0{,}03393\end{aligned}}}
log
c
=
1,978
35
c
=
95
m
,
137
{\displaystyle {\begin{aligned}\qquad \ \ \ \log c&=\ 1{,}97835\\c&=95^{\mathrm {m} }{,}137\end{aligned}}}