|
rr w r t
<br /> TRIGONOMETRIC FORMULAE r.iss
<br /> B B
<br /> o� O
<br /> y ., e a c a e
<br /> - b . .3 7 - d�9 4-
<br /> �.�:} A b C A b o A C
<br /> 3'
<br /> <'�! 3 Right Triangle Oblique Triatrgl
<br /> 3 9Solution of Right Trian
<br /> � gle
<br /> For An A. sin =a ,cw= b ,tae= a ;cot - b,sec=6, cosec= a
<br /> ----- _
<br /> �9 Given red a a b a b a
<br /> 5 , _ x +�
<br /> - en Requi I
<br /> .� --- - a,b A, B,c tan A=—= cot B,c= a _ =a Y
<br /> b + a=
<br /> n ; +
<br /> 7 3 9
<br /> 3 0_3a, a A,B,,b sinA=o =cos B,b=,/ a1—as
<br /> y-s 3 3 JS � �3 A,a B, b, a B=90°—A,b a cot A,a= sin,A.
<br /> _-_ _ __
<br /> fry , �. f b B a a B=90°—A a = btanA a= b
<br /> ----
<br /> , cos A.
<br /> t _3 _ ; A,c B,a, b B=90°—A,a=a sin A,b=c cos A,
<br /> f Solution of Oblique Triangles
<br /> 6797 .- �Jf3 q g
<br /> r
<br /> in C
<br /> �• Given Required a sin B
<br /> G3& s l � , A, B,a b' a, C b= einA 'C= 180°—(A+B),e = '
<br /> sin A
<br /> b sin A °_ a sin C
<br /> A, a, b B, c, C sin B= a ,C= 180 (A t B),a = sin A
<br /> b, C A, B,a A+B-1800—C,tan;(A—B)— a—b)tan (A FBh
<br /> ;';_ c —
<br /> asinC a+ b
<br /> y
<br /> sin A
<br /> k a+b+c I8�)
<br /> b, a A, B, C 8= 2 ,sin JA=J b�,
<br /> sin jB- ,C=180°-,-(A+B)
<br /> ac
<br /> 4 s.s_ J; 'f 4 3 `1 S�,—•y a, b, a Area 8=a �-2 F a,
<br /> S
<br /> --
<br /> ek
<br /> A, b, c Area area = b a A
<br /> a=sin B sin C
<br /> L6gs' ' ?�7y $ 1 ` A,B,C,a Area area =
<br /> 2 sin A
<br /> REDUCTION TO HORIZONTAL
<br /> 9,3 U Horizontal distance=Slope distance multiplied by the
<br /> 7 g SJ 3 ; sf -- .y a e cosine of the vertical angle.Thus:slope distance=319.4 tt.
<br /> S - �ytsoe Vert. angle=b°101. From Table,Page IX.cos 5111Y=
<br /> J Qe e; 8969. Horizontal distance=310.4X.9969=31&09 ft.
<br /> ""y y - y _ 9�t� S10 Aog1e z Horizontal distance also=Slope distance minus slope
<br /> r a
<br /> distance times(1—cosine of vertical angle). With the
<br /> ., ., -, •-- l " yr� ;> Ve name figures as in the preceding example,the follow-
<br /> r, I. / s V,9 Horizontal distance ing result is obtained.Cosine 60 101=.8968 1—.8969=.0041.
<br /> - - = 319.4X:0041=1.31.319.4-1.31=31&09 ft
<br /> 3."- a L-'- % - �:' J __•- f �I /9 When the rise is known,the horizontal distance is approximately:—tbe slope dist-
<br /> y ;.•3'r y') 7, - 4— ance less the square of the rise divided by twice the slope distance. Thus:rise=14 ft.,
<br /> slope distaneezr3020 it. Horizontal didanoe=3026--214 X14_=9-0.32=30228 ft.
<br /> MADE IN U.S.16 -
<br /> i
<br /> y
<br />
|