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h - TRIGONOMETRIC FORMUUR
<br />B, J; B' i
<br />Ab C.
<br />Right Triangle Oblique Triangles
<br />Solution of Right Triangles
<br />For Angle A,. sin = c , cos= o , tan= L ,.cot = a , see = b, cosec -= a
<br />Given Required
<br />P 'i a,b A, 'B ;c tanA=b=cotB'c= a4 { 2=a 1 { a
<br />:t _u 2
<br />.4 a, c• A;B;b einA=C.=cos B,b=�ITe+a)(co?
<br />_ 1 a V
<br />i 1�A a• A b, c B=90°—A, b= a cotA, c= sin A.
<br />i
<br />A,• b B, a, c B = 900—A. a. = b tan A, c = cos A.
<br />1
<br />ru A- B,a; b B=90 A,a=csinA,b'=ccosA,
<br />Solution of Oblique Triangles
<br />`s c Given Required° .
<br />a'sin B ' a'sin C
<br />zaf
<br />s. A, B, a 'b,' c, C L = sin A ' C = 180°—(A { B), o = sin It
<br />h sin A a sin C
<br />a b .. B c C sin B= a., C= 180°—(A i B), c= sin A
<br />'a, b, C-• A, B, o., A+B=180°— C, tangy (A—B)= (a—b)tan 1. (A+B)
<br />Ar. �t. c —asinC a + b
<br />sin A
<br />A, B, C s— 2 ,sin'A=� 8 c
<br />sin 1B—
<br />a+b+c,
<br />b, c Area s — 2 , area .= a (s a 8—) (s c
<br />x 1 b e sin A
<br />!' , b, c Area
<br />A
<br />area = - 2`
<br />a= sin B sin C
<br />A; B, C, a Area area 2 sin A
<br />s
<br />REDUCTION TO HORIZONTAL
<br />t a , Horizontal distance= Slope distance multiplied by the
<br />cosideofthe vertical angle. Thus: slope distance 3t9.4ft.
<br />- tipace Vert. angle=5° 101. From Table, Page IX. cos 5'101=
<br />t day v 9959. Horizontal distance=319.4X•9959 ""918.09 ft
<br />S qie Horizontal distance also= Slope distance minus slope
<br />a distance times (1 --cosine of vertical angle). With the
<br />`le same figures as in the preceding example, the follow
<br />-
<br />Horizontal distance ing result is obtained. Cosine 5° 19'—.8959.7=.8959=.0041.'
<br />919.4X•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 />_s „ ante less the square of the rise divided by twice the slope distance.: Thus: use=14 It.
<br />slope distance=_302.0 ft. Horizontal distance—,30M6— 14 X 14 = 0-0 32=30226 ft
<br />2X3026 d
<br />•a:, .�•s:;�?v.�{"l.'�['.'."1'T..nT- ,r,..,..t�`„.`r-!9R��s .,.�r�-,.,,.,..- PBi3 ._.... r..., »�. �s .
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