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<br /> Right Triangle L— Oblique Triangles 774
<br /> - J V ? '''= Solution of Right Triangles -7 6 0 ---
<br /> b a b i e'4-70 r✓
<br /> For Angle A. sin = c ,cos= cot = a,sec— h, cosec — —
<br /> F le
<br /> a
<br /> Given Required I
<br /> 3 a
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<br /> a, b A, B,c 77 tanA=—= cotB,c = a + 3 =aV
<br /> LJ l " • a (c
<br /> a, c A, B, b sin A=Q=cosB,b=�(c-1 a —a)
<br /> $, b, c =90°— , =acotA = a
<br /> i'
<br /> sin A.
<br /> - - ------- _ a B b
<br /> A, b B, a, c B 90°—A,a = b tan A,c= b /.
<br /> cos A. -
<br /> A,c B, a, b I B=90°—A,a=c sin A,b=c cos A, 7
<br /> r'
<br /> 5 f Solution of Oblique Triangles
<br /> / J A B Given Required a sin B 77Y--- ,a b, c, C b = A , C= 180°—(A { B) c a sin C
<br /> sin sin A
<br /> 2 7 A. a
<br /> -- - c a sin-0
<br /> b B, , c Bing= ,G'= Iso°—(A } B),c= t
<br /> •� c7 y o l •", .4� r��t; a ,,Sjfa A-
<br /> b C A B c A+B=180'—C,tan z(A—B)= a—b)tan A} ,
<br /> a 7 = ry r 3 7 7 J A7 p; c — a sin C a } b
<br /> Q b, a A, B, C 8=a, 2 in JA—`li b .--r
<br /> 77 .14
<br /> sin;B=�a—aXa—c G,=1A0°4
<br /> ab =(A.
<br /> „ r
<br /> �J d• a 188 3' �_ 8�, r V ' +c
<br /> a, c ac '
<br /> : rea vl;a 1- +2 ,area = a(a—a
<br /> A, b, c Area area = b c sin A 7 y b
<br /> r
<br /> 3 y 2 ' j
<br /> sa sin B 8111 C -- .
<br /> 3
<br /> A,B,C,a Area area = ' 7
<br /> 2 sin A
<br /> a REDUCTION TO HORIZONTAL
<br /> Horizontal distance=Slope
<br /> l a distance
<br /> multiplied bee 9y the
<br /> / " 3 ✓ a�stapoe V Hgle verticalcosine of the5 '. angle.
<br /> Table,Page IX cos os 50 1W=
<br /> Suppe di nce=318.4X.8066-- l&o9 ft.
<br /> d ornzontal ata
<br /> A 1e Horizontal distance also= ope distance minus slope
<br /> 4e °g distance times(1—cosine o7vertical angle). With the
<br /> grfigeindseced1Wtll0neifigures
<br /> Co ° example,0he =8LHorizontal distance
<br /> 31&4X.0041=1.31.319.4-1.31=31&09 ft
<br /> When the rise is known,the horizontal distance is approximately:—tbe slope dist-
<br /> _ _ ance less the square of the rise divided by Wee the slope distance. Thus:rise=14 It.,
<br /> slope distanee=302.8 ft Horizsahl distsboe—SMLe— 14=3oy8-0.32=302.28 ft,
<br /> F MADE IM V.$.A. e`
<br /> w.
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