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TRIGONOMETRIC FORMULAE -
<br />B B
<br />c
<br />a a
<br />C—b a G
<br />Right Triangle;
<br />Oblique Triangles.
<br />Solution of Right Triangles
<br />• a)' b a' b c o
<br />1Far Angle A:` sin = G , cos= , tan= L,, cot = , sec = b, cosec = —
<br />1
<br />,
<br />Given
<br />b
<br />Required
<br />A, B ,e
<br />o a a
<br />cy F
<br />to,, A, = = cd, 11, e = " a? $ = a 4 FIT a
<br />a, c .
<br />4., B, b
<br />sin A = =cos B, b =1j (c� a} (c—a) = c 1— a'
<br />s
<br />A, a
<br />B, b, e
<br />B=90°—A, b= acutAc= a
<br />,,
<br />sin A.
<br />A, b"
<br />B, a, c
<br />B=90' _A,a = b tan A ,, e = 8
<br />1
<br />cos A.
<br />A, o
<br />B, a, b
<br />B = 90°—A, a = c sin A, b = c cos A,
<br />Solution of Oblique Triangles
<br />Given
<br />Required
<br />a sin R '
<br />'A B),c=asinC
<br />TRIGONOMETRIC FORMULAE -
<br />B B
<br />c
<br />a a
<br />C—b a G
<br />Right Triangle;
<br />Oblique Triangles.
<br />Solution of Right Triangles
<br />• a)' b a' b c o
<br />1Far Angle A:` sin = G , cos= , tan= L,, cot = , sec = b, cosec = —
<br />1
<br />,
<br />Given
<br />b
<br />Required
<br />A, B ,e
<br />o a a
<br />cy F
<br />to,, A, = = cd, 11, e = " a? $ = a 4 FIT a
<br />a, c .
<br />4., B, b
<br />sin A = =cos B, b =1j (c� a} (c—a) = c 1— a'
<br />s
<br />A, a
<br />B, b, e
<br />B=90°—A, b= acutAc= a
<br />,,
<br />sin A.
<br />A, b"
<br />B, a, c
<br />B=90' _A,a = b tan A ,, e = 8
<br />cos A.
<br />A, o
<br />B, a, b
<br />B = 90°—A, a = c sin A, b = c cos A,
<br />Solution of Oblique Triangles
<br />Given
<br />Required
<br />a sin R '
<br />'A B),c=asinC
<br />sin A sin A
<br />a, b
<br />B, c, C,
<br />b sin Aa sin C
<br />sin B= ,C = 180°—(A t B), c =
<br />4A,
<br />a sin A
<br />a b, C'
<br />A, B, c
<br />A+B=180°—•- C, tan a (A—B)= (a—b) tan (ASB)
<br />ab
<br />$
<br />a sin C
<br />o = -
<br />sin A
<br />a, b, c
<br />A, B, C
<br />.8=a$2 $,c,sin lA=�I s
<br />I'
<br />}�
<br />sin iB—
<br />'a,
<br />a $$ c,
<br />b, c
<br />Area
<br />R= 2 area
<br />b, c
<br />Area
<br />area. = b c sign A
<br />yA,
<br />}'1i,
<br />a- sin B•sin C
<br />B, Ca
<br />Area
<br />area =
<br />2 sin A
<br />REDUCTION
<br />TO HORIZONTAL
<br />_.
<br />Horizontal distance=Slave distance multiplied by the
<br />cc
<br />cosine of the vertical angie. Thus: slope distance =319.-4 ft.
<br />6,516,
<br />cas J° io
<br />From Table, 9=
<br />aHorezontal
<br />:
<br />e
<br />CoQ '�e
<br />9959.�distance -319.4X.9 318.119 ft.IX.
<br />a Horizontal distance also=Slope distance minus slope
<br />distance times (1—cosine of vertical angle). With the
<br />same figures as in the preceding example, the follow -
<br />Horizontal distance
<br />ing result is obtained. Cosine 511 191=.9959.1—.0959=.0041.
<br />319.4X.D041-1.31. 319,4-1.31=318.09 ft.
<br />When the rise is known, the horizontal distance is approximately:—the slope-dist-
<br />inee less the square of the rise divided by twice the slope distance. Thus: rise=i41!ty;
<br />slope disfance=302.0 ft.
<br />Ilorizontai distance=302.6— 14 X 14 =302 6-0.32=302.28 ft.`
<br />�.
<br />2X302.6
<br />- _
<br />MADE 1N V. B. A.
<br />1 -
<br />i.a,
<br />-
<br />-
<br />
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