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3 i• G/. 3 r �- TRIGONOMETRIC FORMULAE
<br /> C
<br /> c a c a C�Y a
<br /> b C t CA C
<br /> Right Triangle Oblique Triangles
<br /> S' Solution of Right Triangles
<br /> For Angle A. sin =a ,cos= b tan= a b c
<br /> ,cot = ,see= , cosec=
<br /> c b a b a
<br /> Given Required
<br /> a
<br /> �j a, b A, B,c tZA= b= cot B,c = a2+ ` = a 1+ s
<br /> 2
<br /> 3 a
<br /> f` a, c A, B, b sin A=c=cos B,b= (c a (c—a) =a 1 ar
<br /> 7
<br /> A,a B, b, c B=90°—A,b =a cotA,c= sin A.
<br /> ��
<br /> G L 7 .. v - 'o A, b `B, a, c B=90°—A,a = b tan A,c= b
<br /> — 2 •'i L ; cos A.
<br /> ay
<br /> 3 Q � � � .s "r ,q, c B, a, b B=90°—A,a =c sin A,b=e cos A,
<br /> Solution of Oblique Triangles
<br /> 3 O Given Required a sin B
<br /> A, B, a b, c, C b = sin A ' C= 180°—(A+B), c= sin A
<br /> b sin A
<br /> /o`1. / i - s-/ A, a, b B, c, C sin B= a ,C= 130°—(A B),c = a sin C
<br /> sin A
<br /> j 'J 3 ° (a—b)tan#(A+B
<br /> a, b, C A, B, c A+B=180 —C,tan (A—B)= —�
<br /> e 1.,;, 2 " a sin C a + b
<br /> 7 —
<br /> 1 sin
<br /> -f ab+
<br /> w S/ a, b, c A, B, C s= 2 ,stn jA=
<br /> J(s—aa ,C=180°—(A+B)
<br /> s ( l t 9
<br /> 7.3 _ - a, b, a Area a=a+2+c,area = s(s—a s—
<br /> /09 f L J
<br /> A, b, a Area area = b c sin A
<br /> �� " i 5•�7 w" ar sin B sin C
<br /> 3 ' } 4 A,B,C,a Area area = 2 sin A
<br /> o g > q j Z, �' f REDUCTION TO HORIZONTAL
<br /> Horizontal distance=Slope distance multiplied by the
<br /> e cosine of the vertical angle.Thus:slope distance=819.4 tL
<br /> Stiarc Vert angle=41 1W. From Table,l'axe`IX.cos b°101=
<br /> o0e 8� a w' Horizontal distance=810.4X. 81$.08 it
<br /> pn8� a orlsbntal distance also=Slopqdistance minus slope
<br /> distance times (1--cosine of vet'dcal angle). With the
<br /> same figures as in the preceding example,the follow-
<br /> Horizontal distance ing result is obtained.Cosine 59 W=.9958.1—.9959=.004L
<br /> When the rise is known,the boorizoata=1.31.
<br /> dis anMce is�ape ximaattelr..—tbe slope dist-
<br /> ance less the square of the Has divided by tn&x the slope distance. Thus:rise=14 fL.
<br /> slope distance=8028 ft Horizontal distauee-8086— 4-8029-0.82=80846 ft
<br /> r '
<br /> 2 X 8029
<br /> KADE lK V.&A.
<br /> vY
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