\fdO'^ - Old Forge Coal Mines

GEOMETRY AND TRIGONOMETRY. 161
(306) From the vertex B^ draw B D perpendicular to
A C, forming the right-angled triangles ADB and BDC.
In the right-angled triangle A D B, A B is known, and also
the angle A. Hence, BD = 26.583 X sin 36° 20' 43' =
26.083X .59265=15.754 feet. ^ Z>=26.583xcos 36° 20'43'=
26.583 X .80546 = 21.411. A C—A Z> = 40 - 21.411 =
18.589 feet — DC. In the right-angled triangle BDC, the
/? Pi
two sides B D and D C are known ; hence, tan C = =
jyp
r^"'^^ = .84750, and angle C= 40° 16' 53'. Ans.
lo. 5o9
o^ BD 15.754 . BC= — . -^—^
in. Ans.
15.754 ^, _ ^, r, ,,
.^o .n, Ko" = aAaKA = ^^-S^, or 24 ft. 4.4
'
sm C sm 40 16 53 .64654
Angle B - 180° - (36° 20' 43' + 40° 16' 53') = 180° - 76°
37' 36' = 103° 22' 24'. Ans.
(307) This problem is solved exactly like problem No.
305.
Sin of 63° 4' 51.8'= .89165.
• Cos
of 63° 4' 51.8' = .45274.
Tan of 63° 4' 51.8' = 1.96949.
(308) .27038 = sin 15° 41' 12.9'.
.27038 = cos 74° 18' 47.1'.
2.27038 = tan 66° 13' 43.2'.
(309) The angle formed by drawing
radii to the
extremities of one of the sides equals — pr-, or 32° 43' 38.2'.
Ans. The length of one side of the undecagon equals
'—
-^ or 4.6364 inches. The radius of the circle equals
i of ^0364 _ 2.3182 " _"
^"^^ '"^^^'- ^"'•
sin of i(32° 43' 38.2') :28l73"
(310) If one of the angles is twice the given one, then it
must be 2 X (47° 13' 29'), or 94° 26' 58'. Since there are
two right angles, or 180°, in the three angles of a triangle,
the third angle must be 180 - (47° 13' 29' + 94° 26' 58'), or
38° 19' 33'.