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<br />�,TRIGONaMETRIC FORMULA
<br />a a a,
<br />9 b
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<br />4� b -614�
<br />Right Triangle Oblique Triangles
<br />6 Solution of Right Triangles
<br />t
<br />For Angle A sin= ,-cos= U , lan= , cot = b , sec = o, cosec = c
<br />c c b a U a
<br />Giver. RequiNd r 2
<br />rd, b 11, B ,c tate _1 = b =cot B, c = 1 = a 1 + �s
<br />1k ?:a, a . 4, B, b sin A = C = cos B,.b
<br />' (L
<br />i' A, a B, b, c 8=90°,4, b — acot_4, C=
<br />bJAI'
<br />%
<br />A, b B, a, c B=9G°—tl,a = Utan4,c—
<br />CU511,,
<br />4, c - V, a, b B= 90°—A, a = c Fin A, b = r cos -4
<br />Solution of Oblique Triangles
<br />Given Required a sin -D "
<br />Al B, a b c G " b = in ;4 ' C = 1S0°—(•i B), e
<br />=b sin .rl. L sin G'
<br />b F,', r., C sing= a ,C .150°=(A { B}, o.= sin Il
<br />a, b, C ' .1, B, c _4 18=180°— Ctap' !, (fl—.Ts) _ (rc—L) tan - (A+B) �•.I
<br />a+ b M) 7J
<br />a sin t:
<br />G L
<br />sin A
<br />a, b, c 4, B, Cs='a+Zc;sin' ._1=
<br />ids—a.11s—c)
<br />sin', B— � a a C_ 180`—(A+B)
<br />rte-b-r�
<br />a, b, c Area 5= area
<br />A, b, c Area area = b c s 1
<br />a= sin B sin. G'
<br />B, C a Area area = 2 sin A
<br />REDUCTION TO HORIZONTAL 1 6 Sl�'��
<br />Horizontal distance -= Slope distance multiple by the
<br />cosine of the vertical angle. Thus: slope distance =319.4 it,
<br />,ace Vert. angle= 51 t0l. From Table, Page IX. cos 51 101=
<br />als 9959. horizontal distance=319.4X.9959=316.09 ft.
<br />��oPe odic Horizontal distance also =Slope distance minus slope
<br />Qe 4 P distance times (l—cosine of vertical angle). With the
<br />same figures as in the preceding example, the follow -
<br />Horizontal distance ing result is obtained: Cosine 50 101=:9959. 1—.9359=.0041.
<br />319.4X.0041=1.31. 319,4-1,31=318.09 ft.
<br />When the rise is known, the horizontal distance is approximately:—the slope dist-
<br />ance less the square of, the rise divided by twice the elope distance. Thus: rise= 14 ft.,
<br />slope distance 302[0 ft Horizontal distance=MX; 14 X 14 302.6-U.32 30223fL
<br />,.
<br />2,X 302.6
<br />- MADE IN U. 9. A. ,; �F
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