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TRIGONOMETRIC FORMULI£
<br /> B B
<br /> a c a c
<br /> a
<br /> 1
<br /> �l, -7 b a d � a A b C
<br /> _ h-�
<br /> Rt� t Triangle . Oblique Triangle
<br /> �_ Solution of Right Triangle a b a b o e
<br /> :! z•5© • For Angle A. sin = a ,cos= e , T,cat- a. =b, cosec=
<br /> r =
<br /> qa
<br /> Given Required �'
<br /> a, b A, B,atan A=8= cot B,c= a=�- =a 1-( s
<br /> a
<br /> a
<br /> J i
<br /> a, a A,B, b '4sinA=o =coeB,b=%/Tc+a (c—a =c 1—a_s
<br /> A,a B' b' c B=90°—A,b=a cotA,o= sin_
<br /> A, b B, a, c B=90'—A,a =b tan A,c= b //�
<br /> os A.
<br /> Cl G N' S•5 CA, c B,a, b B=90°—A,a=c sin A,b= cos A,
<br /> y _ o Solution of Oblique Triangles
<br /> Given Required asin B
<br /> A, B,a b, c, C b= , a= 180°—(A+B),o=asinC
<br /> sin A sin A
<br /> / b sin A °— a sin C
<br /> �{, �'� ? '� � 17� 711 � A' a' b B� c� C cin B= a .�'= 180 (A t B).c =
<br /> sin A
<br /> 7•! :� 3 6 a, b, C A, B, c A+B=180°—C,tan a(A—B)—(a—b)tar ;�A}B)_
<br /> a sin C a
<br /> , sin A
<br /> a, b, c A, B, C s=a+— .in 3A=Nis be—c
<br /> v
<br /> 3_L7_ sin jB Ilx—taNs—c �C=180°—{A+B)
<br /> 3 39 � a+b+c V ao.
<br /> l` 3 Z a, b, a Area s= 2
<br /> D
<br /> _•/6 ......�/ A\
<br /> 5 A, b, e Area area = b c sin A
<br /> 2 0
<br /> z S _ a2 sin B sin C „�—
<br /> Q r n
<br /> 3 3 A,B,C,a Area area = 2 sin A
<br /> REDUCTION TO HORIZONTAL _\�
<br /> Horizontal dishace=Slope distance multiplied piths
<br /> ce cosine of the vertical angle.Thus:slopedistance=9 Ott.
<br /> a�s�s¢ • Vert. angle=50 lo'. From Table,page IX.cos °W--
<br /> 9959.
<br /> Looe Hor2;ontal distance=31&4X.98Bi=S1E 0l1 ft,
<br /> A11; Horizontal distance also=Slope distance minus slope
<br /> o� 3 CJ'7 • ,ve distance times'U—cosine of vertical angle). With the
<br /> � / < same figures as in the preceding example,the follow-
<br /> F Horizontal distance lr4t Mult is obtained.Cosine 60 W--996&1—.9969=.0041.
<br /> 318:4X.9041-1.31.319.4-1.51=31&09 fL
<br /> S 6 1 When the rise is known,the hotizontal distance is appro:imalely:-the slope dist-
<br /> slope
<br /> c, once less the square of the rise divided
<br /> by Wee the do distance Thum rise=l4 ft.,
<br /> y R slope distance=90 6 ft. Horizom*dbUnew4M6—l§4 la—'=q--&32=3OL28f
<br /> SX9E6.i.
<br /> MADE IN Y.S.A.
<br /> r,
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