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J3J• 7 � •
<br /> _ TRIGONOMETRIC FORMULA&
<br /> J B B
<br /> c 91s . f a
<br /> a a JS ,t , a
<br /> A A
<br /> b C �b C � C
<br /> Right Triangle Oblique Triangles
<br /> Solution of Right Triangles
<br /> l n I f For Angle A. sin = ,cos= ,tan= b cot = ,sec= b, cosec= a
<br /> 'j4S Given Required
<br /> _ a, b A, B,c tanA=b= cotB,o = a$T Y =a 1
<br /> + a
<br /> A, B, b sin A=o =cos B,b=�(a-}-a)(o—a) =a a 1—�-
<br /> J
<br /> A,a B, b, c B=90°—A,b =acotA,o= a
<br /> (" sin A.
<br /> i A, b B,a, o B=90°—A,a = btan A,c= b /O
<br /> cos A. 9 X25
<br /> l ✓ x` A, c B, a, b I B=90°—A,a=c sin A,b=c cos Ai—
<br /> Given
<br /> ;
<br /> a Solution of Oblique Triangles 7
<br /> G&vep Required a sin B
<br /> A, B, a b, c, C b = sin A , C= 180°—(A { B), a = sin A
<br /> A, a, b. B,c, C sin B= b sian A'C= 180°—(A+B),c = a sin C
<br /> sin A
<br /> a, b, C A, B, a A+B-180°—C,tan j(A—B)= a—b)tan 1(A+B)
<br /> Ii Y Al � a _ a sin C
<br /> sin A
<br /> b� a g B C s_a.{ b+o,'injA—Nis bQ� ,
<br /> ,.r
<br /> a {s—a1(s—c
<br /> y � �- tr �f .J sin?B= ,C=180°—(A+B)
<br /> ao
<br /> a+b+c
<br /> a, b, c Area a— 2
<br /> A, b, c Area area = b c sin A
<br /> (
<br /> A,B,C,a Area area =a2 sin B sin C _
<br /> 2 sin A
<br /> REDUCTION TO HORIZONTAL
<br /> Horizontal distance=Slope distance multiplied by the Z
<br /> cosine of the vertical angle.Thus:slope distance=319.4 fL
<br /> Vert angle=5°101. From Table,Page IX.cos b°lof
<br /> ca�o0e a o°', 9959• Horizontal distance=319.4X.9959=3&&09 ft.
<br /> ¢gle Horizontal distance also=Slope distance minus slope
<br /> .� qe p* a' distance times(1—cosine of vertical angle). With the
<br /> same figures as in the preceding ex ple,the follow-
<br /> Horizontal distance follow-
<br /> ing result is obtained.Cosine 5°10'= 1—.9959=.004L
<br /> 319.4X.0041=1.31.319.4-1.91=31&09&t
<br /> When the rise is knows,tfie horizontal distanceis approximately:—the slope dist.
<br /> ance less the square of the rise divided by twice the slope distance. Thus:rise=14 ft.,
<br /> ` slope disttnae=3026 ft. Horizontal distaaee�902I— 4 X 14=4M6-0.32=302.28 fk
<br /> .. i 2 X 302.6
<br /> • BADE Ia U.a.A,
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