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DISTANCES FROM SIDE STAKES FOR CROSS-SECTIONING Roadway of any Width. Side Slopes 1 1/2 to 1. In the figure below: opposite 7 under "Cut or Fill" and under .3 read 11.0, the distance out from the side stake at left. Also, opposite 11 under "Cut or Fill" and under .1 read 16.7, the distance out from the side stake at right Slope Stake Side Stake Crad Center Stake Side Stake Slope Stake 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 Cut or Fill Distance out from Side or Shoulder Stake Cut or Fill 0 0.0 0.2 0.3 0.5 0.6 0.8 0.9 1.1 1.2 1.4 0 1 1.5 1.7 1.8 2.0 2.1 2.3 2.4 2.6 2.7 2.9 1 2 3.0 3.2 3.3 3.5 3.6 3.8 3.9 4.1 4.2 4.4 2 3 4.5 4.7 4.8 5.0 5.1 5.3 5.4 5.6 5.7 5.9 3 4 6.0 -6.2 6.3 6.5 6.6 6.8 6.9 7.1 7.2 7.4 4 5 7.5 7.7 7.8 8.0 8.1 8.3 8.4 8.6 8.7 8.9 5 6 9.0 9.2 9.3 9.5 9.6 9.8 -9.9 10.1 10.2 10.4 6 7 10.5 10.7 10.8 11.0 11.1 11.3 11.4 11.6 11.7 11.9 7 8 12.0 12.2 12.3 12.5 12.6 12.8 12.9 13.1 13.2 13.4 8 9 13.5 13.7 13.8 14.0 14.1 14.3 14.4 14.6 14.7 14.9 9 10 15.0 15.2 15.3 15.5 15.6 15.8 15.9 16.1 16.2 16.4 10 11 16.5 16.7 16.8 17.0 17.1 17.3 17.4 17.6 17.7 17.9 11 12 18.0 18.2 18.3 18.5 18.6 18.8 18.9 19.1 19.2 19.4 12 13 19.5 19.7 19.8 20.0 20.1 20.3 20.4 20.6 20.7 20.9 13 14 21.0 21.2 21.3 21.5 21.6 21.8 21.9 22.1 22.2 22.4 14 15 22.5 22.7 22.8 23.0 23.1 23.3 23.4 23.6 23.7 23.9 15 16 24.0 24.2 24.3 24.5 24.6 24.8 24.9 25.1 25.2 25.4 16 17 25.5 25.7 25.8 26.0 26.1 26.3 26.4 26.6 26.7 26.9 17 18 27.0 27.2 27.3 27.5 27.6 27.8 27.9 28.1 28.2 28.4 18 19 28.5 28.7 28.8 29.0 29.1 29.3 29.4 29.6 29.7 29.9 19 20 30.0 30.2 30.3 30.5 30.6 30.8 30.9 31.1 31.2 31.4 20 21 31.5 31.7 31.8 32.0 32.1 32.3 32.4 32.6 32.7 32.9 21 22 33.0 33.2 33.3 33.5 33.6 38.8 33.9 34.1 34.2 34.4 22 23 34.5 34.7 34.8 35.0 35.1 35.3 35.4 35.6 35.7 35.9 23 24 36.0 36.2 36.3 36.5 36.6 36.8 36.9 37.1 37.2 37.4 24 25 37.5 37.7 37.8 38.0 38.1 38.3 38.4 38.6 38.7 38.9 25 26 39.0 39.2 39.3 39.5 39.6 39.8 39.9 40.1 40.2 40.4 26 27 40.5 40.7 40.8 41.0 41.1 41.3 41.4 41.6 41.7 41.9 27 28 42.0 42.2 42.3 42.5 42.6 42.8 42.9 43.1 43.2 43.4 28 29 43.5 43.7 43.8 44.0 44.1 44.3 44.4 44.6 44.7 44.9 29 30 45.0 45.2 45.3 45.5 45.6 45.8 45.9 46.1 46.2 46.4 30 31 46.5 46.7 46.8 47.0 47.1 47.3 47.4 47.6 47.7 47.9 31 32 48.0 48.2 48.3 48.5 48.6 48.8 48.9 49.1 49.2 49.4 32 33 49.5 49.7 49.8 50.0 50.1 50.3 50.4 50.6 50.7 50.9 33 34 51.0 51.2 51.3 51.5 51.6 51.8 51.9 52.1 52.2 52.4 34 35 52.5 52.7 52.8 53.0 53.1 53.3 53.4 53.6 53.7 53.9 35 36 54.0 54.2 54.3 54.5 54.6 54.8 54.9 55.1 55.2 55.4 36 37 55.5 55.7 55.8 56.0 56.1 56.3 56.4 56.6 56.7 56.9 37 38 57.0 57.2 57.3 57.5 57.6 57.8 57.9 58.1 58.2 58.4 38 39 58.5 58.7 58.8 59.0 59.1 59.3 59.4 59.6 59.7 59.9 39 40 60.0 60.2 60.3 60.5 60.6 60.8 60.9 61.1 61.2 61.4 40
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{ "text": "unit no thick des\n22 cont.\n some brown w/ flag\n stones appear above\n 50 feet\n100 ft\ntop ? sequence is\na flasy ss which has\na low shoulder in\nthe hull. 100ft thick\n23 50 ft. dh gray shale\n24. 50 ft.\n 15 ft. ss flagstone\n25 35 ft.\n 50 ft.\n 35 ft. dh gray shale\n pollen sample 85%g\n26 26 ft. ss flagstone\n low shoulder\nbrown weather\n27. 55 ft. black shale w/\n numerous flasy\n interbeds of silt\n```<swale>```<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`<swale>`< [TRANSCRIPTION_TRUNCATED_DUE_TO_LOOP]
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TRIGONOMETRIC FORMULÆ B A B C A B C A C Right Triangle Oblique Triangles Solution of Right Triangles For Angle A. sin = a/c, cos = b/c, tan = a/b, cot = b/a, sec = c/b, cosec = c/a Given Required tan A = a/b = cot B, c = √(a² + b²) = a√(1 + b²/a²) a, b A, B, c sin A = a/c = cos B, b = √((c+a)(c-a)) = c√(1 - a²/c²) a, c A, B, b B = 90° - A, b = a cot A, c = a/sin A. A, a B, b, c B = 90° - A, a = b tan A, c = b/cos A. A, b B, a, c B = 90° - A, a = c sin A, b = c cos A, A, c B, a, b Solution of Oblique Triangles Given Required b = (a sin B)/sin A, C = 180° - (A + B), c = (a sin C)/sin A A, B, a b, c, C sin B = (b sin A)/a, C = 180° - (A + B), c = (a sin C)/sin A A, a, b B, c, C A+B=180°-C, tan(½(A-B))=((a-b)tan(½(A+B)))/(a+b), a, b, C A, B, c c=(a sin C)/sin A s=(a+b+c)/2, sin(½A)=√(((s-b)(s-c))/(bc)), a, b, c A, B, C sin(½B)=√(((s-a)(s-c))/(ac)), C=180°-(A+B) s=(a+b+c)/2, area = √(s(s-a)(s-b)(s-c)) a, b, c Area area = (b c sin A)/2 A, b, c Area area = (a² sin B sin C)/(2 sin A) A, B, C, a Area REDUCTION TO HORIZONTAL Slope distance Horizontal distance Vert. Angle Rise Horizontal distance=Slope distance multiplied by the cosine of the vertical angle. Thus: slope distance=319.4 ft. Vert. angle=5° 10'. From Table, Page IX. cos 5° 10'=.9959. Horizontal distance=319.4×.9959=318.09 ft. Horizontal distance also=Slope distance minus slope distance times (1-cosine of vertical angle). With the same figures as in the preceding example, the follow- ing result is obtained. Cosine 5° 10'=.9959. 1-.9959=.0041. 319.4×.0041=1.31. 319.4-1.31=318.09 ft. When the rise is known, the horizontal distance is approximately:-the slope distan- ce less the square of the rise divided by twice the slope distance. Thus: rise=14 ft., slope distance=302.6 ft. Horizontal distance=302.6-((14×14)/(2×302.6))=302.6-0.32=302.28 ft. MADE IN U. S. A.