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<br /> TRIG NOME�T)�IC F'"UL.AE
<br /> a c >3 1._ a b' a a
<br /> A A /
<br /> b 'S" p C b
<br /> ¢ '/7- y 6-Right T g3,g(� / Oblique Triangles
<br /> Lf ? /3` Solution of Right Triangles
<br /> - S 7 j: For Angle A. sin =a ,cos= b—,tan= a ,cot = 8,sect sec
<br /> 6, co = —
<br /> �7 •�S 9 7 c a b a b a
<br /> 1 Given Required
<br /> �. a, b A, B,c , tan A= b= cot B,c= a + _'a 1 { ar
<br /> a, a A, B, b sin A=a =cos B,b=�(a+a
<br /> c--a)
<br /> a e
<br /> A,a B, b, c B=90°—A,b —a cotA,e= sin A.— L} G
<br /> y b
<br /> / i3 G :^4 J_r, A, b B, a, e B=90°—A,a = b tan A,cJ
<br /> = cos A.
<br /> G
<br /> L C o
<br /> A,e B, a, b B=90°—A,a=o sin A,b=a cos A, c Z
<br /> Solution of Oblique Triangles -'
<br /> Given Required a ein B -a sin C
<br /> 7 a 1 ii fo A, B,a b, c, C b= sin A , C= 180°—(A B), a =
<br /> sin A
<br /> 3,
<br /> Z> A, a, b B, c, C sin B= b sin A,C= 180°—(A t B),a = a sin C
<br /> �.v � / � '
<br /> I l( , O% - ab b, C A, B, e A+B al$0°—C,tan a(A—B)= a—b)a n UA-{-B),
<br /> -J_--- -I
<br /> " a sin ri
<br /> 2'l 3 7 Fs % `f� l J 7,o P- c = sin A
<br /> -- - a' b' a A' B' C 8 +°a'sinjA=Niy plc—c
<br /> sin2B= I(a —
<br /> sae ,C=180° (A+B)
<br /> d, b, a Area s=a+ +a
<br /> 2 , area
<br /> - _
<br /> y' 4 A b c Area b e sin A
<br /> y , area = 2
<br /> ar sin B sin C
<br /> r �-'� A,B,C,a Area area = 2 sin A
<br /> 3 REDUCTION TO HORIZONTAL
<br /> Horizontal distance=Slope distance multiplied by the
<br /> cosine of the vertical angle.Thus:slope distance=319.4ft.
<br /> st�ce u 9orildace319 Page IX cos 61 id� Hrizontaistn = 4X9r5Q 3l&O9 ft
<br /> Max 'Horizontal distance also=Slope distance mines slope
<br /> distance times(i—cosine of vertical angle).With the
<br /> same figuret as in the preeedi��ppgg ezample,the follow-
<br /> Horizontal'V / distance in result fs twined.Cosine bid- .9%9.1—.8869=.0041.
<br /> JSls�XA041= 519.4-1.11=,81&09 ft.
<br /> t When fhe rise is known,the hodmntal'�ance is approximately—the slope dist-
<br /> ance less the square of the rise divided by the slope distance. Ybus:rise=14 ft.,
<br /> slope distance=502.9 ft. Horizontal distanpe_302 0— x-1&=502,6-0,32=392,23 ft.
<br /> 3X 316
<br /> MADE IM U,8,A.
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