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66 . 7'
<br />�¢oo.::S to ,
<br />t b y
<br />00
<br />I t 7— ¢ ¢
<br />I} i
<br />4.T .
<br />TRIGONOMETRIC FORMULtE
<br />•� B B
<br />c a c a c a
<br />1$ b CA b CA b' C
<br />b ,Right Triangle � Oblique .Triangles
<br />Solution of Right Triangles
<br />ll For Angle A. sin = a b a cot= b ,sec = ; cosec = a
<br />b b
<br />j.
<br />c o a a
<br />Given
<br />a,b
<br />Required
<br />A,B,c
<br />a a
<br />tan A=b=cot Ae `sa } a=a 1 } as
<br />a, o
<br />A, B, b
<br />a
<br />sin A = o = cos B, b = %/ (c+a) (c ---a) = c � 1— a �
<br />A, is
<br />B, b, c
<br />B = 90°—A, b = a cot A, c = a
<br />sin A.
<br />A, b
<br />B, a, c
<br />B = 90`—A, a = b tan A, c = b
<br />cos A.
<br />A, a
<br />B, a, b
<br />B = 90°-A, a = c sin A, b = c cos A,
<br />Solution of Oblique Triangles
<br />Given
<br />A, B,a
<br />Required
<br />b, c, C
<br />a sin B , a sin C
<br />b= ,C=180—(A+B),c= sin
<br />sing sin A
<br />A, a, b
<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, c
<br />o (a—b) tan i (A+B)
<br />A+B=180 — C, tan (A—B)= ,
<br />a + b
<br />a sin C `
<br />�
<br />a=
<br />sin A
<br />I(s
<br />a, b, a
<br />A, B, C-
<br />s=a+,sin'-A=
<br />�I b(c—a `
<br />s a s—c
<br />sin'B= ),C=180°—(A+B)
<br />a
<br />Y(
<br />o
<br />a, b, a
<br />Area
<br />a+b+a
<br />s= 2 , area = s(s—a s— (s —a
<br />A, b, c
<br />Area
<br />area = b o s2 A
<br />1
<br />as sin B sin C
<br />I A, B, C, a
<br />Area
<br />_
<br />area 2 sin A
<br />J REDUCTION
<br />TO HORIZONTAL
<br />Horizontal distance = Slope distance multiplied by the
<br />Thus: distance
<br />cosine of the vertical angle. slope =319.4 ft. ,
<br />Vert. angle =5° 101. From Table, Page IX. cos 51 101=
<br />e ais tQ4De
<br />H 9959. Horizontal distance=319.4X.9959=31&09 ft.
<br />ertical
<br />�1e
<br />distance times (1—cosine of vertical angle). With Withlthe
<br />Horizontal distance
<br />same figures as in the preceding example, the follow -
<br />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.
<br />Horizontal distance=3026— 14 X 14 =302.6-0.32=302.28 ft.
<br />2 X 302.6
<br />MADE Ui U. 46 N
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