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41.31 71
<br /> 3S I, 3! tr, 3 s :TRIGONOMETRIC FORMULAE
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<br /> 3', 5.s' _ — Right-T Oblique Triangles
<br /> y! S (, s S• 1 s ` "' cation of Right Triangles
<br /> e� g 7 __ _-3AV �F .�o V ForAngk dta ow= b,tan= a,cot=b,sec=°, cosec= o
<br /> o a b a b a
<br /> Given Re4str4d z s
<br /> S 3 ,'S 3 =� ei ;� a. b A,B,o tan A=-= cast B;o= a -j- a=a• 1 + —
<br /> 3 .It 7 z g o - b a,
<br /> 5w OA=a-ccsB,b=,/ e+a o-a =o_I1-tea'
<br /> V o
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<br /> d,� _ r B=90°-A,b =a cotA,
<br /> � a= .
<br /> 7 sin Aµ
<br /> 8 iz� 96 b
<br /> S_9_g �tO-- Z d, b A 41, o_ B-90°-A,a = b tan A,c.=
<br /> coo A. In /
<br /> 47 , 7 S�`r 2' A.a B,a, b B=90°-A,a=o sin A,b=e cog A,
<br /> L4 , (0 3 q °g Solution of Oblique Triangles
<br /> Given Required a sin B sin d
<br /> SZ 3 4 �-3 ,3 ( Ste/ dd Aasin
<br /> , B,a b,a , C b= . C = 180°-(A+B), a = sin
<br /> .�•�1•----�3 L� 7.3) b sin A
<br /> p S 3 . 3 S --- a, b B,a, C sin B= a ,C= 180°-(A-{-B),a = sin A
<br /> - y e► b, C A,B,o A+B=1800-C,tan'(A-B)- a-b)tan l_(A� B)
<br /> sS7, Ljem— µg a =aginC a-)- b
<br /> 3. �� gin A
<br /> Z/fps/
<br /> a+b+0,sin jA= s- 4--o Z��
<br /> 3 3 3 S-- AA C g= 2 3. ba
<br /> 5. 4. 0y g ` S',{' !o /_� sin JB=�g�a(� ,C=180°-(A+B)
<br /> _ '1- Gw 2 4r e�7 .7 O q b, a Area a g_a+b
<br /> _ 1• v ( 2 , area = ai a
<br /> .S 1 39 S 3♦• 7 3 S�L G s!, b, o '.Acca. area = b a sin A
<br /> 2
<br /> Z U 7. Z 7 r d B C a 1�* �area -at sin B sin C
<br /> c) O S "' , ' , 2 sin A
<br /> REDUCTION TO HORIZONTAL
<br /> (Q Horizontal distance—Slope distance multiplied by the
<br /> cosine of the vertical angle.Thus:slope distance=819.4 tt•
<br /> Vert. angle=51 W. From Table,Page IX.cos 50101=
<br /> oVe 8858•' Hor�•zontal distance=819.4X.9959=81&o9 ft.
<br /> • 5� 1e Iiorizontal distance also=Slope distance minus slope
<br /> r 3 S distance times (1—cosine of vertical Raffle). with the
<br /> J- �L S same tiffures as in the preceding example,the follow-
<br /> 3 $ Horizontal distance ins;result is obtained.Cosine b°Iof=.9958.1—.9959=,0041.
<br /> When the rise is known,t319.4X.0041=1.31.319.4-1.31=31&09 itase iprroiately:-the elope dist-
<br /> ance less the square of the rise divided by twice the slope'distance. Thus:rise=14 ft.,
<br /> ;,slope dfstsaoe8+ 414414
<br /> IF =8066-0 Sfa02 26 ft.
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