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<br />TRIGONOMETRIC- FORMUL./E•
<br />I B B
<br />C a Ca ° a
<br />AA
<br />b C
<br />b C b � C
<br />Right Triangle Oblique Triangles
<br />Solution of Right' Triangles
<br />For Angle Ar sin= a , cos = c b , tan = a , cot = b a , sec = , cosec =
<br />c b b a
<br />Given Required
<br />a, b A, B ,c tan A = by= cot B, c = = a 1 + a2
<br />i a, c -1, B, br
<br />sin A = = cos B, b= \/ (c a) (c—a) = c 11 1 — 02
<br />A, a B, b, e B=90°—A, b= acotA,c= a
<br />sin A.
<br />`•A, b... B, a, c B=90°—A,a = btan A,o= b
<br />cos -4.
<br />A, c B, a, b I B = 90°—A, a = c sin A, b = c cos A,
<br />Solution of Oblique Triangles
<br />Given, Required a sin B a sin C
<br />A, B, a b, e, C b = sin A ' C = 180°—(A + B), c = sin A
<br />b sin A cc ,,in C
<br />A, a, b B, c, C sin B=: a ,C = 180°—(A + B), c = sin A
<br />—b) tan .' (A+B)
<br />I a, b, C A, B, c A-}-B=180°—G', tan 3(A—B)= a
<br />f; a sin C
<br />sin A
<br />C-
<br />a,. b, a A, B, C ` s=a+2+c,,in A=11L3- b)(-s—c)
<br />sin'B=-11
<br />(s—aa cc) C=180°—(A+B)
<br />a, b,'c Area s=a+b+0, area=Vs(x—a (a—b)(s—c)
<br />A, b, c Areanrea = b c sin A
<br />2
<br />7'
<br />a'- sin B sin C
<br />A, B, C, a. Area area =
<br />2 siu A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />ee cosine of the vertical angle. Thus: slope distance=319.4 ft
<br />o Vert. angle= 50 10'. From Table, Page IX. cos 5° 10'=
<br />a`S�p n 9959. Horizontal distance=319.4X.9959=315.09 ft.
<br />ix Horizontal distance also -Slope distance minus slope
<br />ve t• i 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 5'10'=.9959.1-9969=.0041.
<br />319.4X.0041=1.31.310.4-1.31=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 fL,-
<br />Slope distance=302.6 ft. Horizontal distance=302.6— 14 X 14 =302.6-0.32=302.28 fL
<br />2 X 302.6
<br />61ADE IN V.B.A. --
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