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y TRIGONOMETRIC-FORMULAE
<br /> �Z r B B B
<br /> a c a o a
<br /> A A C
<br /> JUght Triangle Oblique Triangles
<br /> Solution of Right Triangles
<br /> a b a b a
<br /> E-For An A. _sin =— —
<br /> _.. i� tan= b ,cot = a,sec=b, cosec=
<br /> _ _ a
<br /> Given RO Oired
<br /> b A .B,a tan A=b= cot B,c = as+ z =a 1 az
<br /> / 0 X 3 ,
<br /> Z4 p 7 a' c A,,,R, b sin A= =coe B,b=V/ c+a (c-a =c 1 a
<br /> yT� A,a B," a B=90°A,b =acotA,a= a
<br /> d � I r- ys [,G 1'
<br /> sin A.
<br /> M.a, a B=90°—A,a = b tan A,c= cos A.
<br /> y 3 6 ,ice �Ly o B,a, b I B=900—A,a=c sin A,b=a cos A,
<br /> 3 9 g o Solution of Oblique Triangles
<br /> 8 J 7 9 3 v (liven Required a sin B a sin C
<br /> 3 / y3G8 A, Aa b, o, C b= ain'A ' C= 180°-(A 1-B), a = sin
<br /> , a, b B,c, C sin B= bsaA.�C= 180°-(A+B),a = sin
<br /> j 7 y ''4R, b, C A, B,a A+B=180°-C,tan;(A-B)- a-b)tan a'+L(A+B)
<br /> b '
<br /> _ a sin C
<br /> 377
<br /> 3'G 3 a sin A
<br /> z .-7 s r c 3 b, o A, B, C s-a+b+main A= (s- a-c
<br /> ZG9 / oc s 7 V f ..�_- 3 2 be
<br /> - x 7
<br /> a,
<br /> 3-it-/v-7 77
<br /> '2-
<br /> �-& :; 4 Z`j sin 2B=J 8�a e ,C--180°-{A+B)
<br /> o _ a+b+c
<br /> y y a, b, a Area a= 2 , area = a a—a s— (a—c
<br /> g s' A b c Area b a sin A
<br /> u7G v3s_�
<br /> , area =
<br /> 2
<br /> 9b `y a2 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 /> lcosine of the vertical angle.Thus:slope distance=519.4 ft.
<br /> °g a Vert. angle=b°101. From Table,.Page IX.cos 60 lot=
<br /> 9989. Horizontal distanoe=S19.4X.9A6 -W&09 fL
<br /> S�oQe Awe Horizontal distance Rho=Slope distance minus slope
<br /> Ve distance times(1-cosine of verticl angle). With the
<br /> } Horizontal distance i
<br /> same
<br /> result is o obtained:in Cosin 50IWQ� M example,.8869the =.0041.
<br /> 7 518.4X.0041=1.51.518.4-1.51=518.08 ft
<br /> When the rise is known,the horizontal distance is aps-admately-the slope dist-
<br /> 1 ance less the square of the ride divided by t,rioe the 81006 distance. Thus:rise=14 ft.,
<br /> �.� slope distance=5026 fL Hori eoW distad -_, 26-= 14-ale-a..=-50226 fL
<br /> X 3016
<br /> MAN IN
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