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<br /> �l S l 6l + TRIGONOMETRIC FORMUL&
<br /> i,3
<br /> (� z� B B B
<br /> �� 6,7� fi.�9 o a c a c a
<br /> S—
<br /> { r C
<br /> 3A
<br /> b C b C�— A J
<br /> Right Triangle Oblique Triangles
<br /> Solution of Right Triangles
<br /> For Angle A, sin = ,cos= ,tan= b ,cot = a,sec=b, cosec= a
<br /> Q ,a Given Required a t—�2
<br /> A, B,c tan A= b= cotB,a = ar f z =a�1+s
<br /> 3? . a, c A, B, b sin A=6=cos B,b=V/(c+a)(c_a)=o
<br /> A,a B, b, c B=90°—A,b =a cot A,a= sin A.
<br /> b 993
<br /> A, b B, a, c B=90'—A,a.= b tan A,e= cos A.
<br /> 7.
<br /> 7✓ A, c B, a, b I B=90°—A,a =:;o sin A,b=c cos A,
<br /> Solution of Oblique Triangles
<br /> Given Required a sin.B a sin C
<br /> A, B,a b c, C b= C= 180°—(A+B), c =
<br /> * 7, ! P sin A ' sin A :
<br /> A, a, b B,qC sin B= bsaA,C= 180°—(A+B),c = sin
<br /> 3 3 �IS, IG 3 3 a, b, C A,B,c A+.&=180°—C,tan 1(A—B)= a—b)ttan+-((A+B)
<br /> s' V . r , _asin C
<br /> sin A
<br /> a+b+6,sin3A=Vis b e
<br /> a, b, a A, B, C 8= i
<br /> q--/.-J - sinaB= I(s
<br /> —aa,a),C=180° - A+B)
<br /> h l $ a3
<br /> a, b, a Area s=a+b+c2 , area
<br /> bcsinA
<br /> / A, b, c Area area = t/ Z
<br /> 7 3 v� as sin B sin C
<br /> A,B,C,a Area area =
<br /> 3 Z sin A 7i 3l
<br /> REDUCTION TO HORIZONTAL
<br /> 2, 717 3, Horizontal distance=Slope distance multiplied by the
<br /> t cosine of the vertical an"Thus:alopedislcoslo.4ft.
<br /> Vert angle—S'101. From Table,Page iXc os 6'i(Y=
<br /> / a ; e�g 9BN HoriZeatat dispncerffi&4X.l�si8oe fL
<br /> Z $fop A9g1e Horiaoutal tante also=Slope diifasce manna slope
<br /> Ve distance times(1—cosine of vertical angle):With the
<br /> I 2,7 saiae figures as in the pebcedt6g example,the follow-
<br /> C Horizontal distance ing result is obtained:Cosine 6°W—.=L I—ABN=.00n.
<br /> 3l.4X.004Y=l.sL Ax9.4—==31iY<Ojt
<br /> When the rise is known,the herisoftd dirtance I 1pprozi�sis;—the slope dist-
<br /> ante less the square of the Rise divided lgtwice the IBope distance us:rise=l4 fL,
<br /> 38 slope distance=302.6ft. Horkea si distams=soZ g._ -4W."32=302.28 IL
<br /> rsos In u.S.ti
<br /> t
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