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7`f / . - TRIGONOMETRIC FORMULAE
<br /> Z83• 7 ' z2-2e,-1 B n B
<br /> ,sv g
<br /> 3y .00 /3 / z .qL fi.t e a Ca a a
<br /> S-d'7�s�
<br /> f ( l / 3 , �J Right TAs e Oblique Triangles
<br /> sv / S�� Solution .ef Right Triangles
<br /> 6•�3 "8or Angie _ ,coo— a b ,tan,,= a ,cot = b,sec= , casee
<br /> o b a b a
<br /> 105 2 %�, r 2- Given at .
<br /> b= cot B,a = a { 9 = a 1 { a
<br /> J 5 •BGG �..Z/ - a, o ein A= =cos B,b=-,/ e-(a a--a =e
<br /> L
<br /> A,.a_, A b, o B=90°—A,b=a cotA,a= a
<br /> sin A.
<br /> - t 7 A.,b B=90°—A,a = b tan
<br /> cos A.
<br /> x8,a, b B=90°—A,a=a:sin A,b=a cos A,
<br /> �/ f � --''L ���✓� l% �7 Solution of Oblique Triangles
<br /> 3 1r, / SC �g3 / 07 Given 4 ..Rimuired b_-a sin B C= 180°—A B a sin C
<br /> A, B,+I� i;;-o, C din A , ( -I- ), a =. sin A
<br /> bsin A' as'inC
<br /> f,� Z. G / jq% A. a, V. B;o, C sin B= a ,C= 180°—(A-f-B),a = sin A
<br /> 7 (a—b tan (A-♦-B)
<br /> -' 'a, b, l� ;.�.B,a A-{-B=180°—C,tan j(A—B)= a-}- b ,
<br /> a sin C
<br /> a sin A
<br /> 2/ �.! aF� v by B,C a=a °,sinA=
<br /> 7. � 2 be
<br /> f 7/ ,� �. 'J s-aKe—o
<br /> .3
<br /> � - �. Lr { sin+)B=V ,C=180'-(A+B)
<br /> 4
<br /> r- - � ���' a-}-b-f-a
<br /> 8= 2 ,area = e s—a s— )
<br /> 3 s—e
<br /> !�' 3
<br /> L S —
<br /> bcsinA
<br /> U �...�.•-n /� r U •Ar bs a � area 2 r'..
<br /> �t C6 :mss.,
<br /> area =a's2 sin
<br /> B B sin C
<br /> Git REDUCTION TO HORIZONTAL 0 ✓1 � r ,j}
<br /> -
<br /> Horizontal.distance aSiopetlislance ttrrtltiPiied by tshe
<br /> r Oesine of the Vertical angle.Thus:slo dtissttance=319.4 ft.
<br /> Af� ` vert.angle=6°id. From Tahte, I7L con fi°10,
<br /> 5 N r� f S o, Optts a Hoorrizontal�isnud cdina noe=�V.4*X� EIiD ns slope
<br /> Q distsaee times (1--cosine of verttca)augk)..With the.
<br /> same figures as In the preceding example,the foAow-
<br /> Horisontal'•distance Ing result is obtsiped.Cosine 60 1 =.9966.1—.9866=:0041.
<br /> 318.4X.0041=1.81.919.4-1.81=31&00 ft
<br /> tlie,iJse is known,the horizontal instance is approiimatel ••—the slope dLat-
<br /> i leas of the rias divide#by twice the slope distance. Thus:rise=l4 ft..
<br /> ft Hotlaogtal distance=802 0-4X1 4 X 30&6 14 31 a4:
<br /> w-
<br /> i
<br /> J ,
<br /> i
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