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TRIGONOMETRIC FORMULAE
<br /> B B �� 7 B
<br /> a a ° a ,z a a
<br /> $j _�--
<br /> v J yb C At —b C A � C
<br /> Right Triangle Oblique Triangles—
<br /> r Solution of Right Triangles
<br /> b (
<br /> .v L `/r For Angle A. sin =�,cos= a,tan= b,cot = a,sec =b, cosec = Q
<br /> Given.. Required a - 2
<br /> �- a, b A,B,a tanA= b= cotB,a = a2+ 2 = a 1 + a2
<br /> `!r 9 a, a A,B, b sin A=Q=con B�b= (a I a) a—a) =a 1—o
<br /> a
<br /> j Z1'o`� f ) ,, 7 �� ( � A,a B, b, a B=900-A,b =a cot A,c= sin A. ,
<br /> A,b B,a, a B=90'—A,a = b tan A,a= cos A. Z
<br /> o B,a, b B=90°—A,a=o sin A,b= o cos A,
<br /> Solution of Oblique Triangles
<br /> Given Required q
<br /> __a sin B ° a sin C
<br /> A, B,a b, o, C b sin A , C= 180 —(A+B),o = sin A
<br /> `- �- b sin A u sin C
<br /> a, b B,c, C sin B= a ,C= 180°—(A {-B),a = sin A
<br /> _ ,
<br /> �. to 's� y A, B,a A+B=180°—C,tan 1(A—B)= a—b)tan'JA+B)�
<br /> a =asin C
<br /> +•
<br /> Z, r
<br /> sin A
<br /> � a
<br /> 1,
<br /> a
<br /> 4 'vt, B, C s= +- °,sin'A=V 3 b a—a
<br /> sin'B=�(s—aale ,C=180°—(A+B)
<br /> a, b e Area s=a+2, area = a(8—a s— )(8—a
<br /> A, b, a Area area = b c s2 A c
<br /> area =at
<br /> C
<br /> B
<br /> Aa2 sin B sin C
<br /> , , , taa �.
<br /> 2sin A rs.
<br /> REDUCTION TO HORIZONTAL
<br /> Hozontal distance=Slope distance multiplied by the
<br /> a cosine of the vertical angle.Thus:slope distance=319.4 ft.
<br /> %' c Vert. angle=5°101. From Table,Page IX,cos b°10/=
<br /> 959.
<br /> m 9Horizontal distance=319.4X.9959=318.0911.
<br /> 3 g;' _ sloesQgle Qy Horizontal distance also=Slone distance minus slope
<br /> distance times (1-cosine of vertical angle). With the
<br /> same figures as in the preceding example,the follow-
<br /> Horizontal distance ing result is obtained.Cosine 50 101=.9959.1—.9959=.0041.
<br /> 319.4X.0041=1.31.319.4-1.31=318.09 ft
<br /> When4be rise is known,the bor*ontal distanceis approximately:—the slope dist-
<br /> ante less the square of the rise divided lei twice the!=distance. Thus:rise=14 ft,
<br /> slope distatioe=302 8 ft. Houfasatal disttsee=3028—14 X 14=902.8-0 32=302.28 ft
<br /> 2X=6
<br /> s.MADE Ia U.&A.
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