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TRIGONOMETRIC FORMULAE
<br /> B B B
<br /> a c a c
<br /> a
<br /> b C
<br /> -
<br /> `q b C A O
<br /> Right Triangle Oblique Triangles
<br /> Solution of Right Triangles
<br /> For Angle A. sin =s ,cos= ,tan= b ,cot = b,sec="a, cosec=
<br /> 1 a b
<br /> Given Required
<br /> a
<br /> C C a, b A, B,c tan A= b= cot B,c = as-F 2 =a
<br /> 1 77.
<br /> 3 L �` ' ,..._ ,p 0 0. a, c A, B, b sin A=c cos B,b=%/ o-{-a o—a =a 1_7 a
<br /> 3 A,a B, b, c B=90°—A,b =acotA,c= a
<br /> sin A.
<br /> �-
<br /> ! A, b B,a, c B=90°—A,a = b tan A,o= b
<br /> cos A.
<br /> A, c B, a, b B=90°—A,a=c sin A,b= c cos A,
<br /> i Solution of Oblique Triangles
<br /> Given Required
<br /> 1 r A, B,a b, o C b _ asinB� C= 1$0°—(A-{-B�,oaasinC
<br /> 3 sin A sin A
<br /> b sin A
<br /> A, a, b B, c, C sin B= a ,C= 180°—(A+B),c = sin A
<br /> C A
<br /> a, B, c A B-1
<br /> zo��J{ z L'r -I — 80°—C,tan z'-(A—B)=(a—b)t+b+B),
<br /> j $ b,
<br /> 4 �o. . b c = asinC
<br /> o sin A
<br /> a+b+c
<br /> f a, f c A, B, C s- i
<br /> 2 ,sn 2A= b e '
<br /> -6 7 f 2- 1 `'f sin 3B— I(s—a0_d C- °
<br /> sin'B=V a c —180 —{A+B)
<br /> a b c
<br /> a, b, a Area s= +2+ , area = s(a—a s— s—c)
<br /> zs �Z
<br /> f ` fe A, b, a Area area = b c sin A
<br /> 3
<br /> 4 } J A,B,Ca2 sin B sin C,a Area area = 2 sin A
<br /> REDUCTION TO HORIZONTAL
<br /> cosine
<br /> oftthtal e rrttiicalangl Thus slopeddistsnce�--319 Chit
<br /> gts9pe Vert. angle=51 101. From Table,Page IX.cos 60 101=
<br /> d 9866. Horizontal distance=319.4X.9869=31&09 ft.
<br /> �o0e Apg�e Horizontal distance also=Slope distance minus slope
<br /> 4e distance times(1—cosine of vertical angle). With the
<br /> same figures as in the preceding example,the follow-
<br /> Horizontal distance in
<br /> —ult is obtained.Cosine 6°10'=.9969.1—.8969=.004L
<br /> 819 4X.0041=1.31.31&4-1.31=31&09 ft.
<br /> When the rise is known,the ltoroontal distance is approximately:—the slope dist-
<br /> ance less the square of the rite divided by twice the slaps distance. Thus:rise=14 ft.,
<br /> slope distance-302.6 ft. Horizontal distance-3o2.6— 4 14 6��V_�28fL
<br /> _ 2 X 302.6
<br /> MADE IN V.s.A.
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