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,�,J AIGONOMET$IC FORMULAE Z 7 <br /> r; .3-D� st3_ $'3 ` � <br /> 3 <br /> lea <br /> C <br /> ` �07 <br /> a ` <br /> ' <br /> a <br /> d' C <br /> b <br /> 15-27 <br /> 36 que Triangles <br /> Ijoisn of Right Triangles <br /> f 5� J. 4- 14 - a b a b a a <br /> cos-1- !. £ a+ a.tan= b,cot-d,sec-b, cosec = a <br /> tand=b- eotB,a, a + =a 1+ a <br /> aiad++'d. <br /> 41r6 - ©6 a <br /> a B °—d b-a cot A,o= <br /> 97asin A. <br /> 5r• lac <br /> o B=90°—A,a= b tan A,c= 3 <br /> -•� ��. 7L. 3>j` 2 -�y cos A. f <br /> a, b B=90°—A,a=csin.A,b=ecosA, '�Cp ,f•Lr-Ny <br /> + ''✓t c_ ._,. x" r Sblution of Oblique Triangles <br /> b=a l!ng C=180°—(A+B a Bsinin AC <br /> C ), <br /> b ein A a sin C <br /> d, A, b a, C sin B= a ,C= 180°—(A+B),c = sin A <br /> - 0 (a—b)tan (4±11 <br /> =b, C ., 'B,a A+B=180°—C,tan (A—B)= <br /> a <br /> in C + <br /> 3011 <br /> '5'� 2.l �� a = sin 29- -J — 4744 <br /> b, a d*B, C s= 2 ,sinjA=V bo , <br /> X47- 34 , �.'�--- sin JB=�s �i� <br /> C=180* <br /> L1 f ©Q� !D /� �7 q a - <br /> 7 9 b, c = , area = --a — <br /> �; d, Arai' 8 2 a s s (se) <br /> / f�.,� �: 1� G� s besinA <br /> d, b, area = 2 <br /> f� y� 4-1 24- -- Zr7. Z �7.� ': a'sin B sin C <br /> B,C,a Area area = 2sin A <br /> x a� 7 /(f¢ f� t / REDUCTION TO HORIZONTAL <br /> V'0,4 -- - l Horizontal distance=Slope distance multiplied by the <br /> l K7�7 7 _ cosine of the vertical angle.Thus:slope distance=919.4 ft <br /> 1¢ �o°o Vert. angle=50 SW. From Table,Page IX.cos 60 10+= <br /> X19 0 9959. Horizontal distance=919..4X.9869=31&09ft <br /> Z J— P��j 1 3J r/¢ Horiz distance also=�distance minus slope <br /> a� 4� ®2•t pe <br /> /Cj_ 1y 5 ve diaGn«times H-coslnc of vertical angle). With the <br /> i( ` / JJ�� same figures as in the op�re ng example,the follow- <br /> ��-Zl 3 1 ,j?' JF(I `- �Q.v HorizontaO'iatan« 81a4X�1=1 3l..SIM-1.31=3A09e 80 ft. <br /> l- =0041. <br /> When.the rise Is known,the horizontal distance is approximately:--the slots dist- <br /> Z" <br /> 16 -G _ - 1 - a sgsaue of the rtes divided by twice tho ado distance. Thus:rise=14 f4, <br /> x93 a ft. Herizontal�i�anor=30x.=—4109.a-0. 30LX 1t. <br /> arJ2oN ° ,. <br /> t • • <br /> OF <br /> 40 <br /> w <br />