\fdO'^ - Old Forge Coal Mines

152 GEOMETRY AND TRIGONOMETRY.
(311) If one of the angles is one-half as large as the
given angle, then it must be ^ of 75° 48' 17', or 37° 54' 8.5'.
The third angle equals 180° - (75° 48' 17' -f 37° 54 8.5'), or
66° 17' 34.5'.
(312) From the vertex B^ draw ^ Z? perpendicular to
A C, forming the two right-angled triangles A D B and B DC.
In the right-angled triangle A D B, A B is known, and also
the angle A. Hence, B i? = sin AxA B = sin 54° 54'
54* X 16^ = -81830 X 16-| = 13.434 feet.
I/O l-o
Sine of angle C = -ytt^ = z-r-rnr = • 99202, and, hence,
x> C lo.o4:Z
angle C= 82° 45' 30'. Ans.
Angle B = 180° - (54° 54' 54' + 82° 45' 30') = 180 - 137°
40' 24' = 42° 19' 36'. Ans.
AD = ABx cos yi = 16-| X cos 54° 54' 54' = 16 :^ X
xZ iZ
.57479 = 9.43613 ft.
CD = BC X cos C = BC X cos 82° 45' 30' = IS^f x
24
.12605 = 1.70692 ft.
AC=AD+ CD= 9.43613 -I- 1.70692= 11.143 = 11 ft.
1 — in. Ans.
4
(313) If one-third of a certain angle equals 14° 47' 10',
then the angle must be 3 X 14° 47' 10', or 44° 21' 30'.
2^
X 44° 21' 30', or 110° 53' 45', equals one of the other two
angles. The third angle equals 180° — (110° 53' 45' -f 44°
21' 30'), or 24° 44' 45'.
(314) Given, BC=437 feet and ^ C = 792 feet, to find
the hypotenuse A B and the angles A and B.
AB= VaT' + BT^= i^792^4-43r = |/818,233 = 904 ft.
6— in. Ans.
4