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XII Natural Trigonometrical Functions7-1 <br />Angie. Sin.' Ten. Sec. Cosec; Cotg. Coaln. Angie. Sin. Tan. Sea Cosec. Cotg. Cosin. <br />32 .5299 .6249 1.1792 1.987 1.600 .84805 -58 39 .6293 .9098 1.2868 1.559 1.235'M715 51 <br />10 .5324 .6289 1.1813 1.878 1.590 .84650 50 10.8318.81 1.25981.5531:228.77531 50 <br />20 .5348 .6330 1.1835 1.876 1.580 .84495, 40 20 .6338 .8195 1.2929 1.578 1.220 .7734 40 <br />30 .5373 .63711,1857 1.861 1.570 .94339 30 30 .6361 .8243 1.2959 1:572 1.213 .77162 30 <br />40 .5398 .641 1'.18791.8531.560:84182 20 40 .6383 .8292 1.2991 1..567 1.206 .76977 20 <br />50 .5422 .6453 1.19011.944 1.550 .84025 10 . 50 .6400 .8342 1.3022 1.5611. 199 .76791 10 _ <br />33 .5446 •64941.1924 1.836 1.540 .83867 57 40 .6428 .83911.3054 1.556 1.192 .76604 50 A° <br />10 .5471 .65361 . i946 1.828 1.530 •83708 50 10 .6450 .84411.30861.5501.1S5 .76417 50 <br />20.5495.65771.19691.8201.520.&3549 40 20 .6472 .84911.3118 1.545 1.178 .76229 40 <br />'30 .5519 .6019 1,1992 1.812 1.511 •83389 '30 30 .6494 .85411.31511.540 1.171 .76041 30 <br />40 .5544 .66611. 2015 1. 804 1.501 .83228 20 40 .6517 .85011,3184 1.535 1.164 .75851 201 1, a22, „^ •ado <br />50 .5568 .6703 1.2039 1.796 1.492 .83066 10 50 .6539 .SG421 .32171.5291:157 .75661 10�`� <br />34 .5592 .6745 1,2062 1.788 1.483 .82904 56 41 , .6551 S693 1.32511.524 1.150 .75471 49 <br />10 .5616 .6787 1.2086 1.781 1.473 .82741 50 10 ,6533 .8744 1.3284 1.519 1.144 .75250 -50 I �' 57 P� /e <br />20 .5640 .6830 1.2110 1.773 1.464 .82577 40 20.6604.87961.33181.5141.137.75058 40 7,'YI; 0 MIN- <br />30 .5664 .6873 1.2134 1.766 1.455 •82413 30 30 .6626 .8847 1.3352 1.509 1.130 .74S96 30r o P/ <br />40 .5685 .G9161.2158 1•.758 1.446 .82248 20 ' 40 .664S S899 1.3386 1.504 1.124 .74703 20 ' <br />50 .5712 .6950 1.2183 1.7511.437 .82082 '10 50 .6670 S952 1.34211.499 1.117 .74509 10 <br />35 .5736 .7002 1.2208 1.743 1.428 .81915 55 42 .6691 .9004 1.34561.4941.111 .74314 48 <br />10 .5760 .7046 1.2233 1•.7361.419 .81748 50 10 .6713 .9057 1.3492 1.490 1.104 .74120 50 <br />.20 .57S3 .7089 1 .2258 1.729 1.411 .815 80 40 20 .6734 .0110 1.3527 1.48.9 17098 .7.3924 40 <br />30 .5807 .7133 1.2283 1.7221..402 .81412 ..30 30 .6756 .91@3 1.3563 1.4501.091 .73728 30 <br />40 5831 .7177 1,2309 1'. 715 I , 393 .81242 ' 20 . 40 .6777 .9217 1.36001.4761.055 .73531 20 <br />50 .5854 .7221 1.2335 1.708 1.385 .81072 ' 30 : b0 .6799 .9271 1.3636 1.471 t.079 .73333 10• <br />36 5878 7265 1 2361 t 701 1 376 50902 54 43, 6820 9325 1 3673 1.4661.072 .73135 47 <br />} 10 <br />.5901 <br />.7310 <br />1,2387 <br />1.695 <br />1.368 <br />.80730 <br />50 <br />10 <br />.6841 <br />.9380 <br />1.3711 <br />1.462 <br />1.066 <br />.72937 <br />50 <br />t �-'�`" � �� <br />20 <br />.5925 <br />7355 <br />1.2413 <br />I,6S8 <br />1.360 <br />.80555 <br />40 <br />20 <br />.GS62 <br />.9435 <br />1.3745 <br />1.457 <br />1.060 <br />.72737 <br />40 - _, <br />� �.�--����-x'- '-- -• ii sin..(; .�. t C <br />30.5948 <br />• P .- <br />.7400 <br />1.2440 <br />1-681 <br />1.3.51 <br />.50386 <br />30 <br />30 <br />.6884 <br />.9490 <br />1.3786 <br />1.453 <br />1.054 <br />.72537 <br />30 <br />p20 <br />C = 1 <br />sin A <br />40 <br />:5972 <br />.80212 <br />20 <br />40.G905 <br />.9545 <br />1-3824 <br />1.448 <br />1.048 <br />.72337 <br />"+ 60 <br />.5995 <br />.7.4451.24661.6751.343 <br />.7490 <br />1.2494 <br />1.6681.335 <br />,80033 <br />10 <br />50 <br />,6926 <br />.9601 <br />1.3863 <br />1.444 <br />1.042 <br />.72136 <br />10 <br />:., b, C <br />A, B, C <br />a+b+C <br />s - A=�I <br />tt " 37 <br />.GOIS <br />.7530 <br />1.2521 <br />1.662 <br />1.327 <br />.79564 <br />53 <br />44 <br />.6047 <br />.9657 <br />1.3902 <br />1.440 <br />1.036 <br />.71934 <br />46 <br />2 ,sin <br />b G <br />10 <br />1.2549 <br />1.655 <br />t.310 <br />.79688 <br />50 <br />10 <br />.G9G7 <br />.9713 <br />1.3941 <br />1.435 <br />1.030 <br />.71732 <br />50 <br />20 <br />.6041 <br />.6065 <br />.7581 <br />.7027 <br />1.2577 <br />1.649 <br />1.311 <br />.79512 <br />40 <br />, 20:6938.97701.39801.4311.024.71529 <br />40 <br />sul 2B-� <br />30 <br />.6085 <br />.7670 <br />1.26N <br />1.6,13 <br />1.303 <br />.79335 <br />30 <br />30 <br />.7009 <br />.9S27 <br />1.4020 <br />1.427 <br />1.018 <br />.71325 <br />30 <br />V a G ,C.=180°-(A+B) <br />A 40 <br />.6111 <br />.7720 <br />1.2633 <br />1 . G36 <br />1.295 <br />.79158 <br />20 <br />40 <br />.7030 <br />.'9884 <br />1.4051 <br />1.922 <br />1,012 <br />.71121 <br />26 <br />`t, <br />a+b+c <br />50 <br />.6134 <br />.7766 <br />1.2661 <br />1.630 <br />1.288 <br />.75980 <br />' 10 <br />50 <br />.7050 <br />.9942 <br />1.4101 <br />1.418 <br />1.006 <br />.70916 <br />10 a, b, c. <br />Area <br />R = 2 area = S(.S-2 8- ) (S- <br />'�� 38 <br />.6157 <br />.7813 <br />1 .2690 <br />1.6211,280 <br />.75801 <br />52 <br />.7071 <br />1. <br />1.414 <br />1.414 <br />1. <br />.70711 <br />45 <br />r i <br />C sin A <br />#, 10 <br />.6180 <br />.7860 <br />t. 2719 <br />1 .618 <br />1.272 <br />.78622 <br />50 <br />A, b, c <br />Areab <br />area = '... ; <br />20 <br />.6202 <br />.790 <br />1.2748 <br />1.612 <br />1.265 <br />:7S442 <br />,40 <br />`� <br />i 30 <br />' <br />.6225 <br />.79541.277S <br />1.606 <br />1.257 <br />.75261 <br />--_30 <br />.. <br />a= sin I3 sin C <br />= ` <br />40 <br />.6245 <br />.8002 <br />1.2803 <br />l G01 <br />1.250 <br />.75079 <br />20 <br />- <br />A B, C, a <br />I <br />Area <br />area <br />2 sin A <br />r •j 50 <br />.6271 <br />.8050 <br />L2S33 <br />1.5951.242 <br />.77897 <br />10 <br />; <br />REDUCTION <br />TO HORIZONTAL <br />y Colin. Cotg. Cosec. Sec. Tan. Sin. Anglo <br />y - - <br />M" <br />Cosin. Cotg. Cosec. 'Sec. Tan. Sin. <br />,I�-, 91 <br />Horizontal distance=Slope distance multiplied by the <br />1gie+li' cosine ofthevertical angle. Thus: slopedislance=319.4ft. <br />Ya�CC Vert. angle -5o 101. From Table, Page IX. cos 51 10'= <br />1 as v 9959. Horizontal distance=319.4X.9069=318.09 ft. <br />C <br />glo4 le = Horizontal distance also=Slope distance minus slope <br />pct. 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-.9968=.0041. <br />319.4X.0041=1.31. 319.4-1.31=318.09 ft. <br />When the rise is knowr-, the horizontal distance is approximately: -the slope dist- <br />nce less:the square of the rise divided by twice the slope distance. Thus: rise =14 ft., <br />ope distance=302.6 ft. lorizontal distance=302.6- 14 X 14 =3026-0.32=802.28 M <br />�.. 2 X 302.6 <br />