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<br /> .. N
<br /> C / TRIGONOMETRIC FORMULA,, Z.........
<br /> }
<br /> 3 B B ly B
<br /> q �.4
<br /> yot
<br /> c a c3 !�
<br /> y sa: A
<br /> C A b
<br /> J 6
<br /> Right Trian le -�
<br /> �. g Oblique Triangles
<br /> Solution of Right Trim;les
<br /> ,.
<br /> or Angle A. sin =-,cos= - tan= e b o e
<br /> t ✓ 3 7 7 F c e , b 4eot= a,sec= k, cosec=
<br /> ? �YT J/ Given Required I :. . a
<br /> a,b A, B,c tan A=b= cotB,c = a
<br /> ♦ = a 1+
<br /> ae
<br /> 1 o y 7 l��l a, c A, B, b sinA=6-eosB,b
<br /> /i H 3 4 / A,a B, b, c B=90°-,d,b=a cots! __ a
<br /> •t' sin A.
<br /> /a9. 7 ' r z� d b B a c B=90°-A a = btanA - b
<br /> , , cos A.
<br /> A,c B, a, b I B=90°-A,a=c sin A,b=c cos A, / �,'� 7
<br /> o /l/, 7% Solution of Oblique Triangles
<br /> Given Required 91 C
<br /> / 0.7 :-y 3 / s .d, B,a b, c, C b= sinnA ' C-180°-(A -F�, c = orcin A
<br /> ' ' 7 J' 3 9•
<br /> 3/j' _ i 7 s Z A, ti, b B,c, C sin g= ,C= 180°-(A-t-B)�e = si C
<br /> a sin'A
<br /> a, b,-C A, B, c A+B=180°-C,tan s(A-B)= a-b)tan'(A+B)
<br /> V.-JV } 7-. asin C a+ b
<br /> sin A
<br /> a, b, c A, B, C a-a+b+c,sinA= ls s-c
<br /> 2 v be '
<br /> 3 � sin B►�(s-a�{s-c C=180 A+B
<br /> a-o
<br /> f c
<br /> b, c Area s=a+b+2 , area =
<br /> J/ 6 7besinA
<br /> 1J"= � A, b, c Area area =
<br /> a
<br /> zs '
<br /> A'B'C,a Area area = 2 e a C
<br /> REDUCTION TO HORIZONT*L
<br /> Horizontd d =Sftspedistance 8iultipiied by the
<br /> oe cosine of the v cal angle,Thus:slope distance=319.4 ft.
<br /> g ?j ajgtap d Vert. settle=8o O'"From Table,Page IX.cos 50 10'=
<br /> So
<br /> „ 9959. Horizo distance=t;9.4XJW=V�,09 ft
<br /> 4 5 mate Horizontal distance,also=Slope distanMoinus slope
<br /> y �e distaneetime!'(1—cosine of vertical an A), with the
<br /> same figures as in the preceding exam the follow-
<br /> t I/ 28 r Horizontal distance in result is obtained.Cosine 5°1d=.9 -yjW=.004L
<br /> 319.4X.0041=1.31.319.4-1.91=338.00 fL
<br /> r` when the rise is known,the bgrizontal distance is approaimatelyt—thetlope dist-
<br /> -' ance less the square of the rise divided by twice the slope distance....Thus:rise=14 fL,
<br /> } slope distance-3X6 ft. HorizonW distan =302.6-0.82-302.28 ,
<br /> Exso:y
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