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<br />, , ,`• - '. TRIGONO.METRIC FORMULfE
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<br />Right Oblique Triangles
<br />_Triangle
<br />Solutiori of Right Triangles
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<br />For Angle A. sin = a ,cos= b ,tan= a ,cot = b ,sec = �, cosec = c
<br />b b a
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<br />c c a
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<br />Given Required a
<br />a,b A,B,c tanA=b=cot.R,c= al } ==a 1+
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<br />a, c 'A, B, b sin A = = cos-B, b =,V(c+a) (c—a) = c 1 — o
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<br />a
<br />A; a B, b, c B=90°—A, b = a cotd, c=
<br />sin A.
<br />c
<br />b
<br />d, b B, a, c B = 90°—A, a = b tan A, c =
<br />cos d.
<br />3 r t
<br />A, c B, a, b B = 90°—A, a = c sin A, &= c cos-4, ^
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<br />Solution of Oblique Triangles
<br />—
<br />! Given Required a sin B ' a sin C
<br />7 A, B, a b, c, C b =
<br />A ' C = 1801—(A + B), c = sin A
<br />sin
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<br />sin A G a sill C
<br />A, a, b B, 0,C sin B= C = 180°—(A + B), c =
<br />d
<br />a, sin
<br />1
<br />a, b, C A, B, e, A+B=180°—C, tan :'(A—B)=(a—b) tan 1(d+B)
<br />t
<br />a + b
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<br />a sin C
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<br />a+b+c ls- b)(—c)
<br />b,. c A; B, C S= 2 ,Sin-2A= 1 b c
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<br />g
<br />sin' B= Il' , C=180°—(A +B)
<br />1 (L C
<br />A
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<br />a, b, c Area s=a+2 ! c, area
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<br />bosinA
<br />A, b, c . .Area area
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<br />2
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<br />a= sin B sin C
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<br />A, B, C, a Area area =
<br />2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance=Slope distance multiplied by the
<br />cosine oft ie vertical angle. Thus: slope distance =319.4 ft.
<br />Vert. angle=51 101. From Table, Page IX. cos 5° 11Y=
<br />'
<br />''<,
<br />9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />s�opc P��le Horizontal distance also=Slope distance minus slope
<br />ye distance times (1—cosine of vertical angle). With the
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<br />��t 06
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<br />ollow-
<br />same figures as in the preceding example, the follow-
<br />Horizontal distance ing result is obtained- Cosine 50 101=•9959.1—.9959=.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 />67.05
<br />°
<br />ante less the square of the rise divided by twice the slope distance. Thus: rise=141t.,
<br />14 X 14
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<br />slope distance=302.6 ft. Horizontal distance=302.6— =302 6-0.32=302.28 ft.
<br />2 X 302.6 •
<br />16
<br />MADE IN U. &A.
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