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<br />TRIGONOMETRIC FORMULAx
<br />B F AI
<br />G a c a c
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<br />Rigbt Triangle Oblique Triangles i
<br />i Solution of Right Triangles -
<br />I
<br />a Ib a b c c;
<br />For Angle A. sin = o , cos = a , tan = b , cot = m , sec = T. cosec = a
<br />Given Required I
<br />72-
<br />b A, B ,o tan A = b =cot B; -a — �/a$ ' = a 1 az
<br />a, c ;A,B,b sinA=a=cosB,b=�/(cIa (e—a)=G�1—ar
<br />. A, a &, b, a.
<br />B=90°—A, b = a cot A, o= a
<br />xin A.
<br />c
<br />b
<br />B = 90°—A, a = b tan A, c=
<br />cos A.'-
<br />:_A,
<br />A,e
<br />B, a, b
<br />B=90° A. a = c sin A, b = c cos
<br />y' Solution of Oblique Triangles
<br />Given
<br />A, B,a
<br />Required
<br />b, c, C
<br />sin {
<br />a B
<br />C=1'80°—(A+B),ca sin
<br />=
<br />bs insin
<br />sin A
<br />i.A, a, b
<br />B,'c, C
<br />b sin A
<br />sinB= ,= 180°—(AB)= 2sinC
<br />C+,c.
<br />a sin A
<br />a. b, C
<br />A, B, o
<br />A+B=180°—C, tan 1 (A—B)—b) tan
<br />a
<br />asin C +6
<br />'
<br />G =
<br />win A
<br />A, B, C
<br />s- a ,ein jA= J{s
<br />N b
<br />sinjB. 6 c— C-180°—(A+B)
<br />a,
<br />b, a
<br />f,
<br />Aiea
<br />a+b+o .
<br />8= , area
<br />2
<br />A, b, c
<br />Area
<br />area = b c sin A
<br />2
<br />_A, B, C, a
<br />Area
<br />a' sin.B sin C
<br />area = 2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />aitx ti0ce
<br />cosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />Vert. angle= 51 101. From Table, Page IX. cos 511V=
<br />` opo
<br />51
<br />M9. Horizontal distance=319.4X.9959=318.09 ft.
<br />Horizontal distance also= Slope distance minus slope
<br />ppgte
<br />ye
<br />distance times (l—cosine of vertical angle). With the
<br />Horizontal distance
<br />xame 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 It.
<br />When the rise is known, the horizontal distance is approximately:—the slope dist-
<br />toce less the square of the rise divided by twice the slope distance. Thus: rise=l4 it.,
<br />Slope distance 14 X 14
<br />-Sao ft.
<br />Horizontal distance=9026— =3028-0.32=302 28H.
<br />—
<br />2 X 902.6
<br />'
<br />MADE In V. 8, A,
<br />
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