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TRIGONOMETRIC FORMULAE
<br /> �9 M
<br /> 7
<br /> fh 'h• y�� B B B
<br /> a
<br /> s A C
<br /> 1b C A
<br /> Right Triangle Oblique Triangles
<br /> Solution of Right Trianglsa
<br /> TorAngle A. An=a = h a
<br /> -Fb= a
<br /> Given a `em a 'tae- b ,cot= u,sec=b, eoseq- •cam
<br /> Required 4
<br /> ab A,B,a tan A=b_
<br /> cot B,tr= i-LI +- s
<br /> a
<br /> y0 7
<br /> Z a' c A, B, b sin d=E s emB,
<br /> p 3
<br /> o
<br /> 3
<br /> A,a B, b, a 8=90°. -A,b =a cold,a= a
<br /> sin A.
<br /> A, b B,a, a B=90°-A,a = b tan A,a= b
<br /> 1 3 cos A.
<br /> A,e B a, b I B.=90°-d a=o sin A,b=e cos A.
<br /> Solution of Obliqus Trfan�lea
<br /> 7 3 (liven Required
<br /> a sin B
<br /> A, B,a b, e, C b= C= 180 a sin C
<br /> _ in.A ' ( ,-I-.�.a= sin A
<br /> "1 416A, a, b B,e, C sin B= b s4 A,C=180°—(A�-B),c = !-sin C
<br /> sin A
<br /> a; b, C* A, B,o A+�=180°-C,tan'z(A-B)- a-b tan I(d+B)
<br /> '� ' � G �••� � • - a = a sin C �
<br /> sin A
<br /> 3 3 a, b, a A, B, C a=a+2+ab
<br /> V,sin3A= s "-°
<br /> �;, a ,
<br /> sin.'B= C=180°-(A+B)
<br /> Area s_a b a, area
<br /> 2
<br /> A, b, a Areab a sin A
<br /> area = 2
<br /> A,B,C,a Area area =as ei_n B sin C
<br /> 77y f� . 28InA
<br /> REDUCTION TO HORIZONTAL
<br /> Horizontal distance=Slope.distanee multiplied by the
<br /> -l�e cosine of the ver°tt"calan¢le•Thus:slopedistm"-31Y••tft,
<br /> ^� v
<br /> Vert.angle==b 101. From Table,Pale IIG cos b°id=
<br /> ML Horizontal distsnoe=,4f¢,4X.>ie68a8
<br /> 51O Apa10 Horizontal di#anee also=Slope distsnee minus al
<br /> Qe e��ss times(1-cosine'of vertical angle). With
<br /> samthe
<br /> d� fignres s0..in the preceding example,the follow-
<br /> Horizontal distance in¢result is obtained.Cosine b°lo,-%M 1-•Aw=.W".
<br /> When the rise is known, 4X8941=1:0.1.319.4-1.51=alas it
<br /> ance leas the square of the s horizontal distance is approxima�e]�-the slope dist_
<br /> t rise divided by tw ice the slope distance Thus:rise=14 ft.,
<br /> Pe distance=802811 Horizontal distanpe=a9a X 14 8-&32=XZ2B ft,
<br /> a x aop:e
<br /> "• YADf to s.s•A.
<br /> y
<br /> 1
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