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Natural Trigonometrical <br />1J <br />1 <br />Angle. Sin. Tan. Sec.. Cosec. Cotg. Cbsin.; <br />1 <br />of ,_ <br />Functions <br />Angle. Sin. Tan. Sec.' Cosec. Cotg. Cosin. <br />o• <br />- <br />of <br />32" ':5299 .6249 1.1792 1.887 1.600 .54805 58 <br />39 <br />.6293 <br />.809S <br />1.286S <br />1.589 <br />1:235'.77715 <br />51 <br />1 " , 10 .5324 .6289 1.1913 1.878 1.590 .84650 60 <br />.10 <br />.G316 <br />.8146 <br />1.2598+1:5&3 <br />1.22S <br />.77531 <br />50 <br />20 .5348 .6330 1.1335 1.870 1.580 .84405 40 <br />20.6338:51951.29291.5781.220.77347 <br />40 <br />30 ,5373 .6371 1.257 1.861 1.570 .84339 .30 <br />30.6361.82431.29591.5721.213.7716'- <br />30 <br />40.5M'64121.1S79I.8531.560.S4132 20 <br />40 <br />.6383 <br />.8292 <br />1.20M <br />1 .567 <br />1 .206 <br />.7G977 <br />20 <br />50 :5422 .6453 1 .1901 1.544 1.550 .54025 10 <br />50 <br />.6406 <br />.8342 <br />1.3022 <br />t.561 <br />I .199 <br />.76791 <br />10 <br />33 1 .6446 .6494 1.1924 1.83 1:540 .83867 57 <br />40 <br />•6423 <br />.a^^3911.30541.5561.192 <br />.7560.4 <br />50 <br />10 .5471 M6 1.1046 11828 1.530 .83708 50 <br />10 <br />.6450 <br />.84411.3086 <br />1.550 <br />1 .185 <br />.76417 <br />50 <br />'I l 20 .5495 .65771 .1969 1.520 1.520 .53549 40 <br />20 <br />.6472 <br />.8491 <br />1.31 IS <br />1.545 <br />1.178 <br />.76229 <br />40 <br />30 .5519 .6619 1 .1992 1.812 1.511 .&3339 30 <br />30.6494.85411:31511.5401.171 <br />.76041 <br />30 <br />40 :5544 .66611 .2015 1,804 1.01 .83223 20 <br />43 <br />.6517 <br />.85911.3134 <br />1.535 <br />1.164 <br />.75351 <br />20 <br />50 .5568 .67031.2039 1.7961'.492 .83066 10 <br />50 <br />.6539 <br />.5642 <br />1.3217 <br />1.529 <br />1.157 <br />.75661 <br />10 <br />34' .5592 .6745 1.20621 1.788 1.453 .82904 56 <br />f <br />41 <br />.65Gi <br />.8693 <br />1.31-511.5-94 <br />1. 150 <br />.75471 <br />49 <br />4 10 .5616 .6787 1.2086 1.781 1.473 .82741 50 <br />10 <br />.6533 <br />,S7441.32S41.510 <br />1.144 <br />.75280 <br />50 <br />1 i :20.5640.68301'.21101.7731.464.83577 40 <br />20 <br />.6601 <br />.8796 <br />1.3318 <br />1.514 <br />1. 137 <br />.75098 <br />40 <br />j 30:5664.63731.21341.76051.455.82413 30 <br />30.6620.88471.33521.5091.1-10.74S9r, <br />30 <br />40 .5683 .6916 1.2158 1.758 1.446 .8221S 20 <br />40.GG48.SS991.33861.5041.124.74703 <br />20 <br />82082 10 <br />I 50.5712.69591.21831.7511.437.820&2 10 <br />50 <br />.0 <br />.667 <br />8932 <br />1. 34211.499 <br />1. i 17 <br />.74509 <br />10 <br />11 <br />j �� I• 35 1.2208 1.743 1.428 55 <br />.12' <br />.G691 <br />.9004 <br />1.3450 <br />1.404 <br />1. 111 <br />.74314 <br />48 1 <br />,I I .5730 .7002 .51015 <br />1 0 .5760 .7046 '1 .2233 1.736 1.419 .81748 50 <br />10 <br />.6713 <br />.01057 <br />1.3492 <br />1.4010 <br />1.104 <br />, <br />50 <br />1J jp•t <br />Nli�'r iy i :20 .5783 .7080 1:2255 1.7291.411 .815SO .40 <br />20 <br />.6734 <br />.9110 <br />1.8527 <br />1. <br />1, 4S,5 <br />1.095 <br />.73931 <br />40 <br />; + 30 1.722 1.402 30' <br />30 <br />.0750 <br />.0163 <br />1.3563 <br />1.480 <br />1.091 <br />:3728 <br />30 <br />•5507 .71331.2233 •51413 <br />'40.5131.71771,23091.7151.393.81232 2.0 <br />40.6777.92111.36001.4761.015.73511 <br />20 <br />50'.5554.72311.38351.7051:356.51072 10 <br />' 50.6799.02711.36361.4711.079.VM33 <br />10 <br />36 :5878 .7265 1.23151 1.701 1.275 .80902 54 <br />43 <br />.6820 <br />.9325 <br />1.3673 <br />1.466 <br />1.072 <br />.7312:5 <br />47 <br />10.5901.73101,23871I. 6951.368:807"u0 50 <br />10.GS41.03S01.37111.4621.066.M37 <br />50 <br />20.5925.73551.24131.6581.360.80555 40 <br />20 <br />.0862 <br />9435 <br />1.3748 <br />1.457 <br />1.000.72737 <br />40 <br />30 .59.48 .74001.24401.651 1.351 .903S6 30 <br />30 <br />.GS84 <br />.94901.37501'.•153 <br />1.054.72557 <br />30 <br />40 .5972 .74401.24661.6751.343 .80212 20 <br />40 <br />.6905 <br />.9345 <br />1.3324 <br />1.448 <br />1.048 <br />.72337 <br />X20 <br />t I� ! 5O .5995 .71901.24M I.G03I:335 .SOMS 10 <br />50 <br />:6926 <br />.0601 <br />1.3S63 <br />1.444 <br />1-0.12 <br />.72136 <br />10 <br />(, 37 .601S .75361.25211.6021:327 .79S64 53 <br />44' <br />.0947 <br />.9G571.3002 <br />1.44011_036 <br />.71934146 <br />10:6041'.75511.2549 1.0551.319 .796S3 50 <br />10 <br />.6967 <br />.9713 <br />1.3941 <br />1.435 <br />1.030 <br />.71732 <br />50 <br />Pkil; 20.6005 .76271.2577II.G491.311 .79512 40 <br />20 <br />.GOSS <br />.0770 <br />1.3980 <br />1.45.1 <br />1.0-4 <br />.71529 <br />40 <br />'30 .6058 .7673 1.2605 1.64.', 1 .303 .79335 30 <br />30 <br />.7009 <br />.9527 <br />1.4020 <br />1.427 <br />1.018 <br />.71325 <br />30 <br />'40 .6111 .7720 1.263 311 .636 1.295 .70153 20 <br />40 <br />.7030 <br />.0584 <br />1.4001 <br />1.422 <br />1:012 <br />.71121 <br />20 <br />50 .6134.77661.26611,6301.238 .789SO 10 <br />50 <br />.7050 <br />.99421.41011.•418 <br />1.GOG <br />.70910 <br />10 <br />38 .6157 .75131.2690 1.624 1.2S0 .78501 52 <br />.7071 <br />1. <br />1.414 <br />1.4141. <br />. <br />.70711 <br />45 <br />i! 10'.6180 786C 1.2710 1.618 1.272 .73622 50 <br />• <br />ra <br />�'• 20.61-02.79071.274S1.6121.265.7S442 40 <br />30.6225.79541.27781.6001.257.5261 30 <br />{ <br />tl { i { ! 40 .G24S .8002 1.2SOS 1.601 1.250 . 76079: 20 <br />50.6271.SO50123351.5951.249.77597 10 <br />1 <br />Cosin. Cotg. Cosec Sea Tan. Sin. Angle <br />Cosln. Cotg. Cosec. Sec. Tan. Sin. Angle <br />'l l t <br />I <br />A, b, c I Areah c sin _-t <br />area = 2 <br />a"- sin B sin C <br />A, B, C,a Area area = 2 sin A <br />REDUCTION TO HORIZONTAL <br />Horizontal distance= Slope distance multiplied by the <br />cosine of the vertical angle. Thus: slope distance =319.4 ft. <br />�N_ vertankle=5°10'. From Table, Page I%. cos 6° IOr= <br />9959. Horizontal distance=310.4X.9959=315.09 ft.Horizontal distance also=Slope distance minus slope <br />distance times (1 -cosine of vertical angle). With the <br />same figures as in the preceding example, the follow - <br />Horizontal distance ing result is obtained. Cosine 5° 101=.9959.1-.9959=.0041. <br />319.4X.0041=1.31.310.4-1.31=318.00 ft. <br />When the rise is known, the horizontal distance is approximately: -the slope dist- <br />ance less the square of the rise divided by twice the slope distance. Thus: rise=14 ft., <br />slope distance=302.6 ft. Horizontal distance=302.6- 14 X 14 =302.6-0.32=302.28 ft <br />2 X 302.6 <br />(LADE IN U. S.A. <br />