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7Y' I'7
<br />.t
<br />'TRI,
<br />METRIC FORMULF-
<br />x ,.
<br />C
<br />A A
<br />b a AI �� �Gb1i ,;r a b
<br />Right Triangle �*. Oblique Triangles ` _ <<
<br />Solution of Right Triangles -
<br />a b�•- a& 1 b c b
<br />For Angle A. sin = c , cos= c ,`tan= b ,cot = a , sec = b, cosec =
<br />a
<br />Given Required a t
<br />a,b A,B,c tail A=b= cot B,c= a F -a 1+a
<br />z
<br />a, c A, B, b sin A = = cos B, b = \/ (c -{-a (c -a) = c 1- v2
<br />'A, a B; b, c B = 90°-A ,, b = a COt.'i, e = a
<br />sin A.
<br />A, b B, a, c B = 900-A, a = b tan A, c = cos A.
<br />A,c B, a, b I B=90°-A,a=csin A,b=ccos A,
<br />Solution of Oblique Triangles / r
<br />9 Given Required _ a sin .l; t
<br />A, B, a b, c, C b sin A ' G = T80° -(A } B), c a sin C
<br />= sin A
<br />�i72 1610 00 coo
<br />b sin A a sin C
<br />A, a, b .77, el'C sin B= a ,C= 180°-(A + B), c'= sin A
<br />a Bio'o ° (a -b) tan (A+171)
<br />b, C A, B, c .:1 �.8=180 - G, tan (A -B)= tL ,
<br />i -a C
<br />......r a sin C +
<br />1.054 .72537 c - sin A
<br />1.048 .72337.
<br />1.042 .72136 i a -1-b -}-G
<br />1 .036 .7193441
<br />a, b, c A,B,C s= 2 Sin 71A=
<br />1.030 .71732
<br />1.024.71529sin iB-
<br />-A B
<br />, 180°�' -F
<br />C )
<br />1.018 .71325 -� ` a c
<br />20 .u92a .73551,24131.b.,b 1.eou .buooa su -.+u .°oa_ :__.._ _-.._.,
<br />%;30.5048.740 1,2440 1.681 1.351 .80386 30 30:1884.94901.37861
<br />40:597..74451.24661.6751.343.50212 20 40 .6905 U545 1,3824
<br />56 .5905 .7490 1.2494 1.663 1.335 .80038 10 50 . G926 .9601 1.3563 t
<br />37 6013 75361 2521 1 662 1 327 .70564 53 44 .6947 .9657 1.3902 1
<br />.7030 .9884 1.406111,:4922�1.012�.7112
<br />.7050 .999 2 1.4101 418 1.000 .7091
<br />.7071 1. 1.414 1.414 1. .7071
<br />Cosin. Cotg. Cosec. -Sea Tan. Sin.
<br />5 is
<br />r
<br />I/ 5E, r
<br />t a+b+c
<br />6 a, b, c. Area s = 2 , area = y7.s(s-a (s - b) (s -c)
<br />t45 >✓ c
<br />� i A, b, c Area area besin -4. t
<br />= 2 ;' v•
<br />az sin Bsin C • S
<br />A, B, C,, Area arca =
<br />0 2 sin A f✓ ;'
<br />REDUCTION TO HORIZONTAL
<br />IIorizontal distance = Slope distance tinultiplied by the
<br />Angle;`�s cosine of the vertical angle. Thus: sIope distance =319.4 it.
<br />Vert. angle =5° 101. From Table, Page IX. cos 5° ]0Y=
<br />N9959. Horizontal distance=319.4X.9959=318.09 ft
<br />gloQc e Horizontal distance also -Slope distance minus slope
<br />distance times (1 -cosine of vertical angle). With the
<br />deb same figures as in the preceding example, the follow -
<br />Horizontal distance Ing result is obtained. Cosine 51 10'=.9959.1-.9869=.0041.
<br />319.4X.0041=1.31. 319.4-1.31=318.09 ft.
<br />i When the rise is known, the horizontal distance is approximately: -the slope dist-
<br />nee less:the square of the rise divided by twice the slope distance. Thus: rise=l4 ft.,
<br />ope distance=302.6 ft. Horizontal distance=302.6-1 XX30IB 8=302,6-0.32=802.28 ft.
<br />MADE IN U7E. A.
<br />1 �
<br />10.6041.75811.25491.6.351.319.79OS8
<br />50
<br />10
<br />20.6065.76271.25771.6491.311.79512
<br />40
<br />20
<br />30 .GOBS .7G73 1.2G05 1.643 1.303 .79335
<br />30
<br />30
<br />40 .6111 .7720 1.2633 1.636 1.295 .79158
<br />20
<br />40
<br />50 .6134 .7766 t.2661 1.630 1.288 .78950
<br />10
<br />50
<br />y
<br />38 .6157 .7,913 1,2690 1.624 1.280 .78SO1 52
<br />10 .6180 .786C 1.2719 1.618 1.272 .78622
<br />50
<br />._ .
<br />20 .6202 .7907 1.2748 1.612 1.265 :75442
<br />.40
<br />30.6225.79541.27781.6061.257.75261
<br />.30
<br />p
<br />40 .6243 .8002 L28031.G01 1.250 .75079
<br />20
<br />50 .6271 .8050 1.2833 1.595 1.242 .77897
<br />10
<br />Cosin. Cotg. Cosec. Sec. Tan. Sin. Angle
<br />.7030 .9884 1.406111,:4922�1.012�.7112
<br />.7050 .999 2 1.4101 418 1.000 .7091
<br />.7071 1. 1.414 1.414 1. .7071
<br />Cosin. Cotg. Cosec. -Sea Tan. Sin.
<br />5 is
<br />r
<br />I/ 5E, r
<br />t a+b+c
<br />6 a, b, c. Area s = 2 , area = y7.s(s-a (s - b) (s -c)
<br />t45 >✓ c
<br />� i A, b, c Area area besin -4. t
<br />= 2 ;' v•
<br />az sin Bsin C • S
<br />A, B, C,, Area arca =
<br />0 2 sin A f✓ ;'
<br />REDUCTION TO HORIZONTAL
<br />IIorizontal distance = Slope distance tinultiplied by the
<br />Angle;`�s cosine of the vertical angle. Thus: sIope distance =319.4 it.
<br />Vert. angle =5° 101. From Table, Page IX. cos 5° ]0Y=
<br />N9959. Horizontal distance=319.4X.9959=318.09 ft
<br />gloQc e Horizontal distance also -Slope distance minus slope
<br />distance times (1 -cosine of vertical angle). With the
<br />deb same figures as in the preceding example, the follow -
<br />Horizontal distance Ing result is obtained. Cosine 51 10'=.9959.1-.9869=.0041.
<br />319.4X.0041=1.31. 319.4-1.31=318.09 ft.
<br />i When the rise is known, the horizontal distance is approximately: -the slope dist-
<br />nee less:the square of the rise divided by twice the slope distance. Thus: rise=l4 ft.,
<br />ope distance=302.6 ft. Horizontal distance=302.6-1 XX30IB 8=302,6-0.32=802.28 ft.
<br />MADE IN U7E. A.
<br />1 �
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