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1 8 2 TRIGONOMETRY.
Angle c may be found by the formula:
c = 180° — (a + b)
c = 180° — (20° 38’ 12" + 41° 33’ 43")
c = 180° — 62° 11’ 55"
c = 117° 48’ 5"
Example 10.
Find the area of a triangle (see Fig. 20), when it is known
that side A is 12.75 feet, side B is 24 feet, and the including
angle C= 117° 48’ 5".
Solution
:
Sin. to supplement of 117° 48’ 5" = sin. 62° 11’ 55" =
0.88456.
C X A X B
Area =
2
Area = 0.88456X12.75X24 = 135. 34 square feet
Example 11.
Find angle c and the sides X and y in the triangle, Fig. 23.
Solution :
c = 180° — (40° + 60°) = 80°
ThesideX= 25Xsin-
40Q
sin. 60°
25 X 0.64279
X=
X
0.86603
16.06975
0.86603 *-
X = 18.556 meters long.
By the use of logarithms the side X is solved thus
:
Log. X = log. 25 -f log. sin. 40° — log. sin. 60°.
Log.X= 1.39794 + (9.808067—10) — (9.937531—10).
Log.X— 1.268476
X = 18.556 meters long.
The side y = 25 X sin ’ 80°
J
sin. 60°
_ 25 X 0.98481
y 0.86603
y — 28.429 meters long.
By the use of logarithms the sidejy is solved thus:
Log. y — log. 25 -f- log. sin. S0° — log. sin. 60°.
Log. y — 1.39794 + (9.993351—10) — (9.937531—10).
Log. y = 1.45376
y = 28.429 meters long.
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