\fdO'^ - Old Forge Coal Mines

GEOMETRY AND TRIGONOMETRY. 155
BC= -$4? = •
sin B sin ^yfi!.o^ 73 54 42
= 16.24 feet = 16 ft. 3 in.
„^ DC 15.603 .«r ^
^^ = t-iH:^ = tan 73° 54' 42- = ^^ ^'''^
A B = A D + 1> B = 27.7^7 + 4.5 = 32.247 = 32 ft. 3 in.
rAB=3'-Z ft. 3 in.
Ans. ] BC= 16 ft. 3 in.
( B=7d° 54' 42*.
(320) In Fig. 8, problem 301, A B is the side of a
regular decagon ; then, the angle C O B = — oi 360°, or 18°.
/C\J
To find the side CB, we have CB = OB X sin 18°, or CB =
9.75 X .30902 = 3.013 inches. Since AB==2x CB, AB =
2 X 3.013, or 6.026 inches, which multiplied by 10, the
number of sides, equals 60.26 inches. Ans.
(321) Perimeter of circle equals 2 X 9.75 X 3.1416, or
61.26 inches. 61.26 — 60.26 = 1 inch, the difference in their
perimeters. Ans.
In order to find the area of the decagon, we must first
find the length of the perpendicular C O (see Fig. 8 in
answer to i? ;
X cos 18°, or {7 (9 = 9.75
X .95106 = 9.273. Area of triangle A O B-\x^.%72>
X 6.026, or 27.939, which multiplied by 10, the number of
triangles in the decagon, equals 279.39 square inches. Area
of the circle = 3.1416 X 9.75 X 9.75, or 298.65 square inches.
298.65 — 279.39 = 19.26 square inches difference. Ans.
(322)
/go 42
The diameter of the circle equals y ^
-f/113.8528, or 10.67 inches. Ans.
The circumference equals 10.67 X 3.1416, or 33.52 inches.
Ans.
In a regular hexagon inscribed in a circle, each side is
1 n P7
equal to the radius of the circle; therefore, —-— = 5.335
inches is the length of a side. Ans.