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1 80 TRIGONOMETRY.
Example 5.
Find the length of the side A when C is 32 feet long, angle
a is 20° 38’ 12" and angle c is 117° 48’ 15".
Note.—Supplement to c is 62° 11’ 55".
Solution
:
Csin. a
A =
A =
sin. c
32 X 0.35242
0.88456
A = 12.75 feet long.
In this example, as in the preceding one, we use the sup-
plement of the angle in obtaining its function, but here it has no
influence on the signs because sin. is positive as well in the
second as in the first quadrant.
Example 6.
Find angle a in Fig. 20, when A is 12.75 feet, B is 24 feet
and C is 32 feet.
Solution
:
B2 1
C2_ A2
cos. a
2BC
242 _j_ 322 _ 12.75s
cos. a =
cos. a
2 X 24 X 32
_ 576+ 1024 — 162.5625
_
1536
cos. a = 0.93583
Angle a = 20° 38’ 12"
Example 7.
Find angle b, Fig. 20, by the same formula.
Solution
:
A2
+ C2 — B2
cos. b = -
cos. b =
cos. b =
2AC
12.752
+ 322 — 242
2 X 12.75 X 32
610.5625
816
cos. b = 0.748238
Angle b = 41° 33’ 43"
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