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3 .3 ,s 4 TRIGONOMETRIC FORMULAE
<br /> o
<br /> �z A
<br /> k b_ C —b a A b C
<br /> 3 - 3; Right Triangle Oblique Triangles
<br /> �'�/' Solution of Right Triangles
<br /> For Angle A. sin =a cos= b tan= a b a a
<br /> a , a , b,cot = a,see=b, cosec= —
<br /> Given Required a
<br /> 3 a b a
<br /> A, B,e
<br /> tan A—b= cotB,e = a2+ 8 = a i77-
<br /> a,
<br /> b as
<br /> a, c A>$ b sin A—o=cos = + —
<br /> _re p, 1? ' / r V o
<br /> B b V a - o--a
<br /> I a 1 a
<br /> A,a B, b, a B=900—A, b =a cotA,c= a
<br /> Y i
<br /> 12 / sin A.
<br /> . 3
<br /> A, b B,a, e B=90°—A,a = b tan A,c= cos A. '.
<br /> d
<br /> A,a B, a, b I B=90°—A,a=c sin A,baa coo A, j Se
<br /> Solution of Oblique Triangles
<br /> 1 s( z G,J) _ A, BGiven a be am b=a sin B C= 1800—(A+B)� c=a sin C
<br /> stn A sin A
<br /> y t : b sin A
<br /> '. A, a, b B,e, C sin B= ,C= 180°—(A+B) a = a sin C
<br /> a '
<br /> sin A
<br /> b, C A,B,c A+B=1800—C,tanA—B--(a—b)tan J(A+B)
<br /> s( )
<br /> a b ,
<br /> A a _ a sin C
<br /> sin A
<br /> b =a+b+a
<br /> o. FU a, , a A, B, C a 2 ,sinA= be I
<br /> a—aXa—a
<br /> ,—
<br /> sin a B=J�,C=180°—(A+B)
<br /> - a+b+a as
<br /> 3 3 a, b, a Area e= 2
<br /> area = 8 s—aT(8—
<br /> w ..�
<br /> A,b, c Area area = b c sin A
<br /> — -
<br /> 2 s
<br /> a2 sin B sin C 'c;
<br /> As B,.E,a Area area = 2 sin A
<br /> REDUCTION TO HORIZONTAL Z
<br /> Horizontal distance=Slope distance mut
<br /> 4
<br /> �piCed^ty the
<br /> r 9 ✓ cosine of the vertical angle.Thus:slope distance=919.4 ft.i1 Vert. angle-50 101. From Table,Page IX.oos b°loi=
<br /> �J 7 o0e d 9969: Horizontal distan0e=3I9.4X.9W—,jl&09 ft
<br /> . '7 �< ),Ole
<br /> � Horizontal distance also=Slope distance minus slope
<br /> distswee times(1--cosine of.vertical angle). With the
<br /> �
<br /> figures as in the preceding example,the follow.
<br /> ��� ----- i3aa1 distance Ing result-is obtained.Cosine b°10'=.9968.1—.9969=.0041.
<br /> the rise is lmo 319:4X.0941=1.si.519.4-1.91=31&09 R.
<br /> 7 safe�tis square of the wn,the horizontal distance is aeproximately:—the slope dist.
<br /> rise divided bT Spice the slew distance. Thus:rise=14 ft.,
<br /> f 9 sl6ge distance= 302.9 ft. HOrimatal distance=502.0— 4 14—,9-0.82-3M23 fL
<br /> 2 X 802.0
<br /> z,g MADE IN U.B.A.
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