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G 7 940 y-69 a .TRIGONOMETRIC FORMULAE V4"
<br /> B J'.J'.7z B
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<br /> ,q%J' B
<br /> a o d a !� o
<br /> S 98I
<br /> .T% 7 T —� b A
<br /> f- 7 C
<br /> q o yo'PS 7 Right Triangle Oblique Triangles
<br /> / '3 6 Solution of Right Triangles
<br /> q8. 3 F! For Angle d. sin-_a ,cos='b ,tan= a ,cot = b sec=°, cosec= °
<br /> Givenn
<br /> 77 7, 11 a b a' b
<br /> a
<br /> / /---� 3 z. 9 S5 9 a, b ,o tan A=b= cot B,o = a4 { s =a 1 ) ar"
<br /> • 2 3" -- t Q *B, b sin A=a=cos B,b=%/ o-F a (o-a =o 1-a�
<br /> ell Sys? S7'no µ. aw A b, o B=90°-A,b =acotA,o= a L
<br /> sin A. 7
<br /> /U�.j3Q . DS� ,_ - 3° + .. :8;a, o B=90°-Aga= btanA,c= b
<br /> 5 JS �/° cos A..3 7 ) c1
<br /> 3 76 9 A0 'A.o ,8,a, b B=900-A,a=o sin:4,b=o coo A, J 1 Z g
<br /> v Solution of Oblique Triangles v- 9
<br /> n Required _ a sin B �-
<br /> • � ooa o a,ou �' / 0 .= A, B,a b, o, C b sinA ' C=.180°-(A+B), o =asinCb ,s'�.
<br /> 3 t I o !'0 C9 y. yL a bsinA sinA
<br /> f y l a o , 1 .Af, a, b $,a, C sin B= ,C- 180°-(A-F,B),c = 'gin C
<br /> a sin
<br /> Op b, C A,B.o A+B=1800-C,tan (A-B)- a-b tan
<br /> t q lJ�"� G U f.674 o =aeinC a+ b3 L
<br /> sin A G
<br /> B, C a=arc e- e-c /U • 2_
<br /> ///. / � / /l ,� ,?� `1 �•71� k. '4 , f ., Z sin JA=
<br /> sin jB=V e-ax� C=180°-(A+B)
<br /> 17µ JJ Jr Z 7 5 ac
<br /> a, b, o Area 8=a+bt, area
<br /> JO.(o J A, b, c Area area a b o sinA y 4-u
<br /> 'L 7 3 •' $ g--7 3. �1 z-- ms sin B sin C _
<br /> J/ //� A,B,C,a Area area = 2sinA Ill. 3 '1
<br /> `-
<br /> /Ct; /--!�'•"/' l J 3 �`t J Ss 3.i' REDUCTION TO HORIZONTAL /
<br /> 7 b y -y} / ! 0 3 0-C Horizontal distance-Slope distance multiplied by the
<br /> 9 3. 7 f ceriine of thevertical angle.Thus:slope distance=919.4 ft,
<br /> o �ts� Vere an¢le=b itY. From Table,Fade IX.cos 60 1W=`
<br /> 9969. Horizontal diatanoe-319.4X.9869=31&09 ft.
<br /> 3' g , v� ` S�v .� Ana�e Horizontal'distance also=Slope distance minus slop
<br /> Qe disionee times (1-cosine of vertical angle). With the
<br /> p I same H�ntes ae in the preceding example,the follow-
<br /> ` 7 Horizontal distanee ins result is obtained.Cosine b°10'=.9859.1-.9868=.0941.
<br /> 0 C / J ! 9 When the rise is known,the 4LoX0.Iziwr&i distance ance is J1=318.09
<br /> P xin teiy-the slope dist-
<br /> the leas the square of the rise divided br twins the dittan6e. 3hns:rise=l4 fL,
<br /> rt.
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