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TRM(;*6METRIC FORMULAE +
<br /> B g
<br /> ii
<br /> a
<br /> ;.. a a a
<br /> •
<br /> i3 t7 db C A b C
<br /> Right Triangle Oblique Triangle,
<br /> Solution of Right Triangles
<br /> t 9 _ For Angle A. sin =a,cos tan= b ,'cot = b,sec= o a
<br /> ,
<br /> 7 c % (liven Required a b> cosec= -
<br /> a
<br /> fir s . A,B,a tanA=b= cotB,c = a
<br /> z ar
<br /> a+ a A,B> b sin A= a =cos B,bc—a
<br /> a �( T=a�1—a;
<br /> A,a B, b, a B=90--A,b=a cot A,a= a °
<br /> sin A.
<br /> A, b B, a, c B-900-A,a = b tan A,c= b
<br /> V d,e B,a b cos A.
<br /> 3 i y B=90•-A,a=a sin A,b=c cos A,
<br /> a Solution of Oblique Triangles
<br /> . (uvea Required .
<br /> A, B, a b c, C b= a sin B
<br /> F in A • C= 180°--(A +B), c= asin C
<br /> J I b sin A sin A
<br /> A, a, b B,'c, C sin B= a ,C= 180°—(A-p•B),a = a sin C
<br /> sin A
<br /> b, C A, B,o A+B=180°—C,tan;(A—B)—La—b)tan A+B
<br /> c = asin C a+ b >
<br /> sin A
<br /> a, b, o A, B, C s=a+2
<br /> Y be
<br /> c + +c, area
<br /> sin;B—Y("—aKs�),C=180°—(A+B)
<br /> 0. b
<br /> Area s=a b = Yes
<br /> —
<br /> 2
<br /> A, b, c Area b a sin A
<br /> area =
<br /> 2
<br /> d>B,C,aa
<br /> I Area area = 'sin—B si�C
<br /> 2 sin d
<br /> �. REDUCTION TO HORIZONTAL
<br /> Horizontal distance—Slope distance in by the
<br /> aY9t9aoe Vent.. asine n¢lee vertical6 . Thus.slopedistanceoo X919.4=
<br /> From Table,Page IX.oa go 10+=
<br /> . X008 �
<br /> Horizontal distance=81&#X.9D6ga3180B ft.
<br /> D4 Horizontal d' pe.distance
<br /> ve distance times(i—cosine of vertical anQle�With 1the
<br /> same figures as in the preceding example,the follow-
<br /> 319-4X-0041
<br /> distance Ing result is obtained-Cosine 5010,=.
<br /> Wires the rise is known, 318.4X.0041=1.31.319.4-1.31=31&09 ft, 1—'9M—'�•
<br /> the horizontal distance is approximately.-the slope dist-
<br /> Oe leas the square of the rise divided by twice the slope distance. Thus: slope
<br /> =l4 ft,
<br /> ve dMance-3026 tL- Horizontal distan 14 14
<br /> oe=300 6-2 X302.6=-'ft6—a32=30228 ft,
<br /> . MMB IM U.S.A.
<br /> t i
<br /> '
<br /> 4
<br /> • • L; / r v ' t
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