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---3--- _� 6 TRIGONOMETRIC FORMULAE
<br /> \( �� f 9 B k B
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<br /> .r3.p41J77 39 y 4y a aa a a
<br /> > >� ' 3. z zl' '54j � �. fG d a C
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<br /> 1'7 f y 7, 7 ` /,/? o s 6 Right Triangle C Oblique Triangles
<br /> O tog 3,N '7 7 f 73 ry A Solution bof Right Triangles
<br /> 7.r 7 a�r3 Por Angle A. sin = e ,cos= o ,tan= b ,cot = b,sec= , cosec=
<br /> Z D, O (liven Required a b a
<br /> / 7 f t' 9 L ,a a b A, B c tanA=a
<br /> 9 Al L _ •. b= cotB,c = a + r =a 1•+_
<br /> 1 o _1 •j/` 0 0 b o a
<br /> 9 0• / 3 I o" 0 A, B,'b sin A=a=cosB,b=V c+a a—a =0 1—os 1
<br /> Ufa, Lf �3Ss" 31' /uG1� a u'a A,a $ b, 0 B=90°A,b =acotA,6= a
<br /> >• 117 sin A. f ti 3
<br /> A( `— ' 8 / d 4' J o A, b B,a, •a B=90°—A,a= b tan A,a= b /
<br /> Tx 7 0 3 cos A.
<br /> 7.!- S L d' A, ° B, a, b B=900—A,a =o sin A,b=0 cos A, 7'/ ?
<br /> i-s"3 f rr,r v / 3 7 ✓ Solution of Oblique Triangles
<br /> (liven Required 7�- 3 L
<br /> —'__----- r Y� �' 3 �-v p a sin B
<br /> A, B,a b, c, C b = , C= 180°—(A+B), 0= ""�C �6-
<br /> l !1 r✓.z y / f Q g q z sin A sin A 7 Z
<br /> q b� sin A
<br /> � -Q p A. a, b B,c, C sin B= a ,C =180°—(A-f B)'., = i
<br /> s A
<br /> 7 L �I >f 0/'f`o U C c a, b, C A, B,a A+B=180°—C,tan j(A—B)—(a—b)tan}(A+B).
<br /> foo a a 1 Cf7 )� d+ b
<br /> a%sinC _
<br /> sin A
<br /> a A, B, C a=a+b+O,sin3A=Yfs s—a
<br /> 7 O VVV b 0
<br /> ____)sin;B— l —( ,C=180°—(A+B)
<br /> / p Z j 1,1 t�j v a, b, c Ares s=a �-a, area = s s—a a—
<br /> s--a
<br /> A, b, a Area area b e sin A
<br /> / O 1 � 7 O = 2
<br /> —.�0 1 + 7 a2 sin B sin C
<br /> 3 Z i A,B,C,a Area area —
<br /> .l1G O' 2sin A
<br /> 'r' 3 /,v• yr/ REDUCTION TO HORIZONTAL
<br /> J/S'. Lr Horizontal distance—Slope distance multiplied by the
<br /> 9ce cosine of the vertical angle.Thus:Slope distance=319.4ft.
<br /> Ve0. Ie=6°1Wge. From Table,PaIX.oos 6°W=
<br /> j ! L? ops 1e c 9866 HorizontaLdi4tanoe=919.4X.9860=91&00fL
<br /> rl� V A Horizontal distance also=Slope distance minus slope
<br /> - Qe distance times(1—cosine of vertical antt��17. With the
<br /> same figures as in the preceding saample,the follow-
<br /> s �' 3 �' Q AIINFizontal distance Ing result is obtained.Cosine bo 10,=.9660,1—.9868=.00tL
<br /> 'GPLea khe tise is]rnovrn,�e&4X.0041=1.91.81&4-1.91=91&00 ft.
<br /> sgptal distance is approximately:—t6 slope dist-
<br /> \ n\ anee less the sq_ a of the rise divided by Wee the slope distance. Thus:rise=14 ft.,
<br /> cgs diatanoe=8026 ft. Horizontal divtanae-002,e—14 X 14=11—IM99=900,88 ft.
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