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<br /> YvOrke-IS o e 4� G D�
<br /> B B
<br /> >h,r r ,q
<br /> a
<br /> —b c A b a
<br /> 1 Rigkt•Tz3angle Oblique Triangles
<br /> �� YZ Solution of Right Triangles
<br /> Lir For Angle A. sin =o ,cos= a,tan= b ,cot = a,sec=b, cosec
<br /> ( ' Given Required a
<br /> ya,.b A, B,c tanA= b= cotB,c = a� } s = a 1+�s
<br /> 3-8 t a, c A, B, b sin = a=cos B,b (F+a c—a =e�1—al
<br /> .ve
<br /> a g, b, a B=90°—A.b= a cotA,c=
<br /> sin A.
<br /> B,a, c B=90°—A,a = btan A,c= conA..
<br /> ----� —
<br /> • A, c B,a, b B=90'—A,a=c sin A,b= c cos A,
<br /> of Solution of Oblique Triangles 3'_�-7
<br /> 7 d O Given Required a sin B 9 3 r
<br /> A, B'a b, c, C b = sin A ' C= 180°—(A } B), a = ein A 3
<br /> b sin A
<br /> � Ceti / / CClGy�7 It G 7�L f A> a, b B, c, C sing= a ,C= 180°—(A 1 B),c = — �
<br /> sin
<br /> 6 $7
<br /> 6-7
<br /> - 'b, c A, B,c A+B=180°—C,tan-(A—B)= a—b)tan 1(A+B)
<br /> a+ b ,
<br /> U- y1� Ct4 asin C
<br /> /a7� �,,,,� � a sin A
<br /> b, a A, B, C s—a+2+c,sinA=�t� btu ,
<br /> sin'B=N�a—aa(c C_180*-
<br /> Al , b, c Area 3=a+b+c, area =1/8(s—a & (e---)
<br /> t�L fyP,ST Or, e f, S.,e47 2
<br /> Q� f0 s �` .�Li �Q! "' A+ b, c Area area = b e s2 A
<br /> A,B,C,a Areaa
<br /> area =
<br /> =sin B sin C
<br /> 2 sin A
<br /> REDUCTION TO BORIZONTAL
<br /> 7• 5 (� �f3 ����~' +-a �' Horizontal distance=Slope distance multiplied by the.
<br /> cosineofthe verticalangle.Thus:slope distance=319.4 ft. `
<br /> 5 �aQce m Vert. angle=51 101. From Table,Page lX.cos 60 101=
<br /> 1995% Horizontal distance=319.4X.9969=31&09 fL
<br /> Novi Horizontal distance also=Slope distance minus sin
<br /> T h ge distance times (1—cosine of vertical angle). With
<br /> same figures as in the preced�ng,example,the follow-
<br /> Horizontal distanse ing result is obtained.Cosine 6 101=.9988.1—.9988 7AM.
<br /> A319.4X.0041=1.31.319.4-1.31=31&09 ft.When the rise is known,the horizontal distance is approximately:=the 2104 dist.
<br /> S' r moe less the square of the rise divided by twice the slope distance. Thus:rise=14 ib,..;
<br /> elope distance- .eft H0MwNsWA tanee= MS.. 6.6 1t
<br /> • - RADE IN U.S.A. .4
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