Laserfiche WebLink
5 <br />'TABLE 11�COntiiaueld <br />TRIGONOMETRIC FORMULAE (continued] <br />In- any Irm'ngle: <br />Given a, b? Ce to find C, B., A. <br />Use Law of Lines. <br />Given A, B, c; to find a, b, Ca <br />Use Law of Lines. <br />Given a, b, cr Ce <br />to find A, B, <br />+ b + em�- a) b) wwom- C) <br />Let s <br />-- 2 = <br />s(s <br />cos mVA= bo —' <br />r <br />tan Y2 A s ---~n <br />9 —New 8 <br />r <br />tan Y2B== ordom <br />r <br />t/C= $,o <br />Area of a triangle: <br />Area = j 1c) ab Sin C <br />Area — s (s--- a) s — b) (a — c) <br />RISMOIDAL FOIi.MULA. <br />Vol. = h (B+b+4AI) <br />h � altitude; b� B am bs�ses; M � midsection <br />,,0%M.VN.-00afY 0 <br />TABLE No. 9. <br />o find Tangent and External for curve of <br />any other degree, divide by degree of curve and <br />M column of corrections.add correction found <br />Degree of curve with a given I. <br />by da 4 0 <br />ividing <br />given tangen <br />the dis <br />the curve is <br />may b,e found <br />tangents or external oppos <br />to (or external),. <br />ite I 1)y <br />tance from a point on the tangent to <br />very nearly the square of the tangent <br />length divided by t <br />vice the radius. <br />ti <br />j � r <br />I <br />r <br />'TABLF, IV <br />USEFUL RELATIONS. <br />Linealf. <br />X . 000 19 <br />miles <br />Lineal <br />yards <br />X.0006 <br />miles <br />Square <br />inches <br />X.007 <br />feet <br />Square <br />feet <br />X.111 <br />square yards <br />Square <br />yards <br />x.0002067 <br />acres <br />Acres <br />X 4840 <br />square yards <br />Cubic inches <br />X.00058 —cubic <br />feet <br />Cubic Feet <br />X .03 7` 04 — <br />cubic yards <br />Links <br />X.22 <br />Links <br />X.66 <br />Feet <br />X1.5 <br />links <br />3600 —1 <br />216001 1296000" <br />cnctirfnno <br />Are of 10 (radius <br />Are of 1' (radius -- 1 ) --- . <br />Are of 1" (radius = 1) = . <br />= 3-il-41592654 <br />017453292 <br />000290888 <br />000004848 <br />1 0*564190 <br />4 <br />t <br />4 = 0.,785398163 - - - -V 1.240700982 <br />7C = 0.523598776 07z = 9*869604401 <br />6 <br />4 = L 12837'9167 ; � = 0.101321184 <br />Af <br />17 <br />= 0.523598776 1.772453851 <br />6 <br />4.76 = 4.188790205 - 1 = 0.3183099 <br />3 <br />Curvature of Earth's surface about 0.7 feet in 1 mile <br />Curvature in feet = 0.667 (Dist. in mi1es)2 <br />Difference between arc and chord length, 0. 05 feet in I I % miles <br />Probable error of a single observation = 0-6754 :;� <br />n --- 1 <br />Error in chaining of 0.01 feet in 100 feet.a <br />Due t o----Mn- <br />1. Length of tape error of 0.d1 feet <br />2. Alignment. one end 1.4 feet out of line <br />3. Sag of gape at centre of Q. 61 feet. <br />4. Temperature difference of 150 <br />5. Difference of pill of 15 lbs* <br />STADIA REDUCTION FORMULIE.. <br />Horizontal Distance — R �-- R sing a -r C cos a <br />Vertical Distance � R Y2 sin 2 a + C sin a <br />distance from Ob;,-.-,.,ct glass to crass hairs <br />R -== Readin X distance between cress hairs W <br />Cdista= nce from Object glass to crass hairs + eli►stance f <br />glass to center of instrument. <br />a = angle of elevation for mid Reading <br />F.. <br />rom Object <br />s <br />