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<br /> / o,i -�- S 3 s „'-•-i^ TRIGONOMETRIC FORMUL)E
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<br /> j r� 9 7 lSI3 / o•y < x.89 '����`V /G,3/ 3y,� ¢- / B
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<br /> 6 Triangle Oblique Triangles
<br /> �� p t 7 ` ` y /- 1 3 Solution of Right Triangles 3,fa
<br /> Is.71 v -- a A. sin =a ,cos= b ,tan= a cot = b sec- a
<br /> i } n ,s-, 3 3 0 , g c c b ' a, 7-4x.ec=
<br /> 3,9 f / o•G o° /S Y8 !/ ! f ?Gi n Required
<br /> a n a, b A, B,a tan 19 _-- cot B c = az s z�_
<br /> 0 7 �. ? 1 y y b ��_=a 1+ ¢z '--�•
<br /> -7 a, e A, B, b � sinA=4=cos B,b=�(a �a (�-a a �
<br /> 3 S
<br /> 'A,a B, b, c B=90°—A,b =acotA c= a
<br /> -- q
<br /> sin 4• L r
<br /> y G -� -
<br /> i
<br /> FF
<br /> i 3 r- a ' /,ca y, , _� S 1- A, b B,a, a B=90° A a = btanA c=
<br /> q 5 6 y a' cos A.
<br /> 2.,v b //.7 / j z A,c B,a; b B=90°—A,a gcsin A,b gcCos A / S
<br /> -LL r j ,6 S / �/p !v, 7 Solution of Oblique Triangles ,/1
<br /> 7 " 9vy�9 4 ,4 / Given Required asinB
<br /> , B, a b, a, �' b = C= 180° a si
<br /> A sin A ' —(A B}, c =
<br /> d L t o 3 `x.615 s t,r �, l # b sin A sin A 7 4 7
<br /> i /0.?-9 A_o / s C, 1 7 A, a, b B,c, C sin B= a ,C= 180°—(A f B),,, = a sin C
<br /> sin A
<br /> �" ✓ /Z 7 Z� *r�p- 3 1 9 c I a, b� C A,A e A+B=180°—C tan A—B __ a—b)tan'(A}B)
<br /> f 7 /.i,� 9
<br /> - e �_ t 3 ) •"7`! C s 3 $ 8 l. 1 Z- //,•2,? 9,/ z a sin
<br /> a+ b J3
<br /> ti / 3 ✓ v ..mss ra ,� ( �l, Z/ 7.I y L/ r sin A4.
<br /> v
<br /> q b, a A, B, C s= ;>
<br /> ±aJA Y 7
<br /> 3 /� s �l f7 / /•7 =_�',. : 3's Fre
<br /> sing- ,C-180'—(A+B)
<br /> 4,A9 a, b, c Area + , area =v/ (s—a s—z.
<br /> A, b, c Areac sin A q6 az sin B sin C!o , 7 �� A,B,C,a Area 3 /d� 71
<br /> 2sinA
<br /> REDUCTION TO HORIZONTAL 3,Q 7
<br /> Horizontal distance=Slope distance multiplied 77
<br /> / /./r Y �eof}�eve6ticalangle Thus:slope distance=319.4ft
<br /> 7 Vert an¢1e=6 10. From Table,Pane IX.cos 6°1W=
<br /> - e .8969. Horizontal distance=819.4X.9969=31&09 fL
<br /> F' -7 L ' `' S�oV Ap6�e Horizontal distance also=Slope distance minus slope
<br /> 7 s J"-'-v -, ' ; qe distance times(1-cosine of yy!(ical angle). With the
<br /> n '7 _ � � H`�'f same ftgnres as in the prec nq example the lol1ow-
<br /> 1 3, 3 Horizontal distance ing result is obtained.Cosine 6°10'=.9869,1 9859=.0041.
<br /> ? - 2 819.4X.0041=1.33194
<br /> ance -1.x1=1t&09 ft
<br /> tit.tpl rise is known,the betizontal distance is aaprozimately:-the slope dist-
<br /> _ i leas the square of the rise divided by twice the elope distance. Thus:rise=l4 ft,
<br /> slope'distanoo=902.821 Horizo11W'&dan"-=*-14 X14_6026-0.32=802.28 ft
<br /> `!y' 2X902.6
<br /> 7'
<br /> '�- MADE IN U.8.A.
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