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TRIGONOMETRY. 183
Example 12.
Find angles c and b and the length
of the side X \n Fig. 24.
Sin. c =
Sin. c =
42 X sin. 54°
35
42 X 0.80902
35
Sin. c ~ 0.9T082 r- is meiei
Angle c — 76° 7’ 26"
Angle £ = 180° — (54° 0’ 0" 4- 76° T 26") = 49° 52’ 34’
Side^T =
X =
35 X sin. 49° 52’ 34"
sin. 54°
35 X 0.76465
0.80901
= 33.08 meters long.
By means of logarithms the side X is solved thus :
Log. X = log. 35 4- log. sin. 49° 52’ 34" — log. sin. 54°.
Log.X= 1.544068 4- (9.883463—10) — (9.90795S—10).
Log.X= 1.519573
X = 33.08 meters long.
Note.—The angle c is obtained by interpolation thus : In
the table of trigonometrical functions the sine 0.97100 corre-
sponds to the angle 76° 10’ and the sine 0.97030 corresponds to
the angle 76°. Thus, a difference of 0.00070 in the sine gives
a difference of 10’ = 600" in the angle.
The sine to angle c is 0.97082
The nearest less sine in the table is 0.97030 corresponding
to angle 76° 0’ 0".
Difference, 0.00052
Therefore when an increase in sine of 0.00070 corresponds
to an increase of 600" in the angle, an increase of 0.00052 will
600 X 0.00052
= 446’ 0° 7’ 26’
increase the angle
0.00070
thus, the angle corresponding to the sine 0.97082 must be
76° 7’ 26".
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