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178 TRIGONOMETRY.
Solution of Oblique=Angled Triangles.
Fig. 20.
Oblique-angled triangles
A (see Figs. 20-21-22) may be solved
by the following formulas
:
Solving for Any Side.
C sin. a B sin. a I
n „,_ ^ _
A = — =—
—
T = -\ B 2
+ C1 — 2 B Ccos. a
Z? =
C =
sm c
C sin. £
in. ^
A sin. 3
sin. £•
A sin. <r
sm. a
B sin. c
Jc* + A*—’2A Ccos.i
sin. ^
Solving for Any Angle.
Cos. # =
. , A A
Sin. a — sm. b —– — sin. ^ —
-
B B
Sin. £ = sin. c -_ = sin. # —
-
c -^
Sin. c = sm. <z —- = sin. £ —
= 180° — (£ + *•)
^ = 180° — {a + b)
b = 180° — {a + c)
Cos. £ =
Cos. c =
2 ^4 B cos. £
^ + C* — ^2
^2 4- C2 ^2
2.4 C
A2
+ £ 2 -
2.4 B
Area
Solving for Area.
sin. c X A X B _ sin. a X C X B _ sin. £ X .4 X C
2 2 2
Example 1.
Find the length of the side C (see Fig. 20) when angle a =
20° 38’ 12", angle <r = 117° 48’ 5", and side A = 12.75 feet long.
v
Note.—The angle c exceeds 90°, therefore the supplement
of the angle must be used, which is 180° — 117° 48’ 5"’ =
62° 11’ 55".
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