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<br />TRIGONOMETRIC FORMULAE J
<br />,1J� yrs �vA
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<br />c a c -- -- a c a
<br />ig� � A A C
<br />b aa b
<br />b
<br />_Right Triangle � Oblique Triangles
<br />Solution of Right Triangles
<br />a b a, b c c
<br />For Angle A. sin = o ,cos ,= Q , tan= b , cot = a , sec = b, cosec =
<br />(liven Required
<br />b A,B,c tangy=b=cotB,c= a= } _=a 1+ az
<br />.,a; -a
<br />a; -a A, B, b sinA=c =cos B,b(c+a)(o—a)=c�1—Qi
<br />A, a B, b, c •B=90°—A, b = a cot A, c•= a
<br />� sin A.
<br />t
<br />A, b B, a, e, B =90'—A, a = b tan A, e = b
<br />cos A.
<br />A, e B, a, b B = 90°—A, a = c sin A, b = e cos A.
<br />Solution of Oblique Triangles
<br />(liven Required
<br />A, B, a b, c, C b' = a sin B � C = 180°—(A + B), c = a sin C
<br />sin A sin A
<br />b sin A a sin C
<br />A, a, b B, c, C sin B = a , C = 180°—(A + B), c — sin A
<br />a, b, C A, B, e A+B=180°— C, tans (A—B)=(a—b) tan z (A+B)
<br />a+b
<br />• e=
<br />a sin C
<br />sin A
<br />a+b +c 1 =
<br />a, b, c A, B, C s= 2 ,sin;A— be '
<br />in ; B= J(s—sal ) , C=180°—(A+B)
<br />? a, b, a Area s = a+2 + c , area =1/s (s—a s—) (s—e
<br />y bosinA
<br />A, b, a Area area = 2'
<br />all sin B sin C
<br />A, B, C, a Area area = 2 sin A
<br />' REDUCTION TO HORIZONTAL
<br />s Horizontal distance= Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slope distance =319.4 tt.
<br />taupe Vert. angle =5° 101. From Table, Page IX. cos 51 ID'=
<br />ass 9959. Horizontal distance=319.4X.9959=318.09 ft
<br />51pQp gxe N horizontal distance also=Slone distance minus slope
<br />Vp . Iv a 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. 319.4-1.31=318.09 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=3026— 14 X 14 =3026-0 32=302.28 ft.
<br />2 X 3026
<br />MADE IN U. S. A.
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