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TRIGONOMETRIC FORMULAE i s 17'30 "
<br /> 'B B X13, B
<br /> 3 � ✓ o � /
<br /> c
<br /> a ° a7 3y ° a
<br /> A b C A C
<br /> `Right le Oblique'Triangles 3 t
<br /> Solution of Right Triangles 116
<br /> cli
<br /> For Angl' min =G,cos= a,tan= b,cot=a,sec=b, cosec
<br /> (`
<br /> ! Given uired
<br /> a, b;4` ,B,c taa A= = cot B,c = as T , = a 1 } a
<br /> _ $
<br /> r 4s
<br /> sin A:e=cos B,b=�/ c a (c—a)
<br /> 02
<br /> - - 1,A
<br /> , b, c A,b = A,c= a
<br /> B=
<br /> c j V b a, c; e— acct sin A.
<br /> x9,71 b
<br /> y ^ . 3 i 9 , a>o a B=90°—A,a = btan A,c= cos A.
<br /> a, b B=90°—A,a = c sin A,b=c cos A, L a 1 _,x
<br /> S rJ i utio Oblique Triangles
<br /> _
<br /> n of O iqu T ' ngle
<br /> Requireda tin B a sin 6 Z / z
<br /> A: b 6 C b+a , ---, C = 180°—(A+B),c =
<br /> s i� A sin A
<br /> SG. c >,.'.z A, k 'B,c, C sin B' asaA,C= 180°—(A+B),c = sin
<br /> s
<br /> g A, B,c A{B=180°—C,tan 2(A—B)= —b)do a bA+B),
<br /> a sin C +
<br /> sin
<br /> A, B Va+b+c,sinj,4=' be c ,
<br /> l �Nv
<br /> vG L I 1 uyLn� sin1jB=,l( — K �,C=180°—(A+B)
<br /> S V
<br /> ( ' _a+b+c
<br /> G
<br /> 0 2 , area= a(s—a a— s—c
<br /> �as'6�- bosin A
<br /> 1? - 9i area = 2
<br /> Ys
<br /> 7,/ 2 area a2 sin B sin C j y
<br /> ea = 2 sin A
<br /> 4 L
<br /> REDUCTION TO HORIZONTAL
<br /> 4-A 2 - EDU
<br /> Horizontal distance=Slope distance multiplied by the
<br /> cosineoftheverticalangle.Thus:slopedistance=319.4ft.
<br /> �r� c { i /iv cope Vert. angle=60 101. From Table,Page IX cos 60 10�=
<br /> fes_ ( ) d 9959. Horizontaldistance=319.4X.9959=31&0911.
<br /> r. T " °y Horizontal distance also=Slope distance minas slope
<br /> distance times(1--cosine of vertical angle). With the
<br /> same figures as-in the preceding eaamDle,the follow-
<br /> - 1 :. H ,diatanee in
<br /> result is obtained.Cbsine 51 10'=.8966.1—.9869=.0011.
<br /> ,
<br /> 09 y 319.4X.0041=1,31.319,4-1.31=31&00 ft.
<br /> rise is known,the bgrizontsl distance is approximately'—the slope dist-
<br /> quare
<br /> id
<br /> square of the rise divided by twice the slope distance. Tkms rise=14 ftp,
<br /> sl =302.6 ft. Hor6wntal distaneo--=6—= a309.8-0:3 2--=2811.
<br /> r
<br /> t
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