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<br />TRIGONOMETRIC FORMUL2E
<br />B B
<br />c a c a c a
<br />g b C A b C A b C
<br />I `
<br />Right Triangle Oblique Triangles
<br />Solution of Right Triangles
<br />For Angle A. sin = a , cos = c b , tan= va , cot = b , sec = o , cosec = o
<br />c b, a b a
<br />Given Required a z
<br />a, b A, B ,c tan A = b = cot B, c = a2 + s = a 1 + as
<br />r
<br />?. a, c A, B, b sin A = =cos B, b = �/ (c+a) (c—a) = c 1— o
<br />A, a, B, b, c B=90°—A, b = a cotAto=- sin A.
<br />A, b B, a, c B =90'—A, a = b tan A, c = b
<br />cos A.
<br />A, e B, o, b I B =90'—A, a = c sin A, b = c cos A,
<br />Solution of Oblique Triangles
<br />Given' Required
<br />a sin B a sin C
<br />A, B, a b, c, C b =. C = 180°—(A + B), c =
<br />sin A sin A
<br />b sin A a sin C
<br />A, a, b B, c, C sin B= a , C = 180°—(A + B), c = sin A
<br />(a—b) tan (A+B)
<br />a, b, C A, B, e A+B=1801— C, tan 3 (A—B)= a 11 b ,
<br />=a sin C
<br />' o
<br />sin A
<br />a, b, o A, B, C s = 2 ,sin zA=-V
<br />be ,
<br />sin 2B= �I a c C=180°—(A+B)
<br />a, b, c Area s = a+2 +c , area = -,Is(s—a s— (s—c
<br />A, b,- c Area erea = besin A 2
<br />az sin B sin C
<br />A, B, C, a Area area = 2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slope distance=319.4ft.
<br />`9oce Vert.
<br />angle= 51 101. From Table, Page IX. cos 50 10'=
<br />e ass y 9959. Horizontal distance=319.4X.9959=31&09 ft
<br />'pe,
<br />Horizontal distance siecminusistance slope x distnetimes(lcine of vertical angle).Witht
<br />ve same figures as in the preceding example, the follow -
<br />Horizontal distance ing result is obtained. Cosine 51 10'=.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 />ance less the square of the rise divided by twice the slope distance. Thus: rise=14 ft.,
<br />slope distance=302.6 ft. Horizontal dist4n6e=3026— 14 X 14 =3026-0.32=302.28 ft.
<br />2 X 302.6'
<br />MADE M V. 8.14
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