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TRIGONOMETRY. l8l
Example 8.
Find angle c, Fig. 20, by the same formula.
Solution
:
COS. C = A2
+ B2 — C2
2AB
COS. C — 12.752
+ 242 —322
2 X 12.75 X 4
rrvz.
738.5625 — 1024
612
cos. c = — 0.46640
Supplement to angle c = 62° 11’ 55", and angle c = 117° 48’ 5"
Note.—The negative cosine indicates that it is in the sec-
ond quadrant, therefore the angle is over 90°.
The angle corresponding to this cosine is the supplement
of angle c. To obtain angle c, the angle of its supplement must
be subtracted from 180°.
Example 9.
Find angles a, b and c in Fig. 20, when side A is 12.75
feet, B 32 feet, and C 24 feet.
cos.. ^2
+ C2 -^2
2BC
cos.* = 322 + 242 - 12- 75i
2 X 32 X 24
cos.,^ 1437- 4375
1536
cos. a = 0.93583
Angle a = 20° 38’ 12"
Angle b may be found by the formula
:
sin. b = sin. a
A
sin. b — sin. 20° 38’ 12" —
A
sin. b = 0.35244 X 32
12.75
sin. b — 0.35244 X 1.8824
sin. & = 0.66343
Angle b — 41° 33’ 43"
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