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TRIGONOMETRIC FORMULtE
<br />�S
<br />$ B B
<br />}r
<br />a � �S d� .� a e a ° a
<br />Right Triangle Oblique Triangles —,—J
<br />Solution of Right Triangles
<br />J ;For Angle A. sin = o , cos = ,tan = b ,cot= a ,sec = b , cosec =Y °—a
<br />Given Required a a
<br />,OD
<br />m,b A,B,c taaA=b=cotB,c=1+ a2
<br />� c A, B, b sin A = o = cos B, b — �/ (c a (c—a) = c
<br />0099.oFO o
<br />1�
<br />o11 ,� /
<br />t 0
<br />tO
<br />'00711 A,d
<br />j -
<br />A, b
<br />A; e
<br />Given
<br />a, b
<br />B, b,'c
<br />B=90°—A, b = acotA,c= a
<br />sin A.
<br />B, a, c
<br />B = 90°—A, a = b tan A, c = b
<br />cos A.
<br />B, a, b
<br />B=90°—A,•a=csin A,b=ccos A,
<br />Solution of Oblique Triangles
<br />Required
<br />b, c, C
<br />b = a sin B C = 180°—(A + B), c = a sin C
<br />'
<br />Bin A sill ,A
<br />B, c, C
<br />b sin A a sin C
<br />sin B = , C = 180°—(A { B), c =
<br />a sin A
<br />A, B, c
<br />A+B=1800— C, tan ; (A—B). (a—b) tan 1(A A+B)
<br />a sin C
<br />— sin A.
<br />A, B, Cs=a+2+0,sin
<br />JA=
<br />V(s—. b�c—C
<br />sini;B=((s—aw c ;C-180°—(A+B)
<br />a-(- b +c
<br />a, b, e, Area •s= 2 , area= s(s—a s— (s —c
<br />A, b, c Areaarea = b c sin A
<br />2
<br />a' sin B sin C
<br />A; By C, a Area area = 2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />°c Vert. angle =5° 101. From Table, Page IX. cos 51 101=
<br />4e ass y 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />5
<br />%G APy1e a Horizontal distance also=Slope distance minus slope
<br />Ve 11 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 50 101=.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 ar U.S.A.
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