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/a VSs S U,S.
<br />TRIGONOMETRIC FORMULIE
<br />` B B B
<br />c ¢ c a c a
<br />A. b CAA b C d b C
<br />MADE W Y. 8. 16
<br />Right Triangle
<br />Oblique Triangles
<br />Solution of Right Triangles
<br />For Angle A.' sin =
<br />,cos = a b , cot = a , sec = b , cosec =
<br />(liven
<br />a, b
<br />Required
<br />A, B
<br />az
<br />tan A = = cot B, c = az + z = a 1 TTI
<br />,c
<br />b
<br />a, c
<br />A, B, b
<br />sin A = a = cos B b , (c+a) c—a az
<br />03
<br />A, a
<br />•B, b, a
<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,c
<br />B, a, b
<br />B=90°—A,a=csin A,b=ccos A,
<br />Solution of Oblique Triangles
<br />(liven
<br />Required
<br />a sin B "sin C
<br />A, B, a
<br />b, c, C
<br />h = C = 180°—(A' B), c =
<br />sin A sin A
<br />A, a, b
<br />B, c, C
<br />b sin A ,tl = 180°—(A } B), c =a in C
<br />s
<br />sinB=
<br />a sin A
<br />a, b, C
<br />A, B, c
<br />A+B=180°— C, tan i (A—B)= (a—b) tan ? (A+B)�
<br />a + b
<br />a sin C
<br />c=
<br />sin A
<br />I(s—
<br />a, b, o
<br />'A, B, C
<br />s=a+2+c,sin'A
<br />b(a
<br />sin;B=VIv(3—aa(sc C=1800—(A+B)
<br />v
<br />Ea, b;' c
<br />Area
<br />4=a+2+o, area = s(s—a s— )(s—c
<br />b, c
<br />Area
<br />b c sin A
<br />area =
<br />2
<br />as sin B sin C
<br />A, B, C, a
<br />Area
<br />area =
<br />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 />tQX�0
<br />a ,S0
<br />Vert. angle =5° 101. From Table, Page IX. cos 50 10'=
<br />Horizontal
<br />s1 040
<br />y 9959. distance =319.4X.9959=318.09 ft
<br />Horizontal distance also =Slope distance minus slope
<br />An�r-e
<br />Q0
<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 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. Tbus: rise=l4 ft,
<br />slope distance=302.6 ft
<br />Horizontal distance=302.6— 14 X 14 =302.6-0.32=302.28 ft.
<br />2 X 302.6
<br />MADE W Y. 8. 16
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