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<br /> 7 2 z yG TRIGONOMETRIC FORMULIE i��,�y 00
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<br /> aA A C
<br /> ' C C b
<br /> Right Triangle Oblique Triangles
<br /> 3 L 9 t y .r ✓ P 3 P 4 a__6_S Solution of Right Triangles 3 6 g
<br /> For Angle A. sin =a cos= b tan= a cot= b sec =6 cosec= o e f
<br /> 3f 39. � A �. 3 Z c , c , b , a, b,
<br /> j t s, ?,9 v----- (liven Requireda 2 a
<br /> 3. G L a, b A, B,c tanA=b = cot B,c = a2+ 2 = a 1 + as
<br /> A, B, b sin A= = ll
<br /> cos B,b a:
<br /> A,a B, b, c B=90°—A b =a cotA,c= a a
<br /> ? 4',f 4 sin A.
<br /> 1
<br /> 7 1 A+b B,a, a B=90°—A,a = b tan A c= b /+ 41 y,r"
<br /> s A.
<br /> A,a B, a, b B=900—A,a=c sin A,b=c cos A,
<br /> %a i ;
<br /> a 0 a 7, / Solution of Oblique Triangles
<br /> tltaea Required
<br /> 'A, B,a b, a, C b=asin B C= 180'—(A+ B) a — asinC
<br /> 3 Z _ rain A '
<br /> �? �_ - �' �. '/ sin A
<br /> A, a, b B, c, C sin B= b sin A C,= 1800—A B a sin C
<br /> r a =
<br /> a ( f ), sinA
<br /> i
<br /> " �' .$ k a, b, C A, B, c A+B=180°—C,tan'(A—B)— a—b)tan a(A+B)
<br /> y v 3 y L ) a sin C
<br /> a sin A �-!
<br /> .4 b._c. A, B, C s=a+b+a,sin'A=
<br /> 2 b e 2 3 3 z'
<br /> .
<br /> 3
<br /> sin'B=V 180b—(A+B
<br /> c Area S=a+b c, area a7(7—a
<br /> �. ✓s G q" A, b, c Area area = b c sin A
<br /> 3_ S' 7 5 g -G L = A,B,C,a Area area =a2 sin'B sin C 7 s
<br /> �S. o 3 ,
<br /> REDUCTION TO HORIZONTAL
<br /> Horizontal
<br /> distance=Slope distance multiplied by the
<br /> o cosine of the vertical angle.Thus:slope distance=319.4 ft.
<br /> j S / —_..6! •4 S} // S" it (� a1star a Vert. angle=50 10+. From Table,Page IX.cos 56 lot--
<br /> Y
<br /> o'=.
<br /> 3� ^(� ( 7 S�oPe 1e 9959. Horizontal distance=319.4?C 9959=$18.09 ft.
<br /> `F _„__,• 3 `f ,,,.�, •,�' a .prg a Horizontal distance also=Slope distance minus slope
<br /> Y Ll rt 9 3 �e distance times (1—cosine of vertical angle). With the
<br /> same figures gores as in the preceding example,the follow-
<br /> 0.11Horizontal distance log result is obtained.Cosine 50 10'=.9959.1—.9959=.0041.
<br /> 310,4X pp4l=l.31.319.4-1.31=318.09 ft.
<br /> ' 3 " f When the rise a known,the horizontal distance is approximately:—the slope dist-
<br /> _ 7 ance less the square of the rise divided b7 twice the slope distance. Thus:rise=14 ft.,
<br /> J` p o slope distance=302.6 ft. Horizontal distane@=L3M6—14 X 14=302.6-032=80228 ft.
<br /> 2 X3026
<br /> ( ��•� MADE IN U.B.A.
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