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TRIGONOMETRIC FORMULR_
<br />JT 1> B
<br />a c a c a
<br />AA�b C A b C
<br />Right Triangle, Oblique Triangles
<br />Solution of Right Triangles
<br />a b a b c c
<br />For Angle A. sin = o ,cos = ,tan = b ,cot = ,sec = b , cosec = a
<br />Given Required I
<br />a, b A, B ,c tan A = b = cot B, e = -V-a—'2+-Xy = a I f az
<br />a, c A; B, b sinA= =cos B,b=�)c1—
<br />/(c+a c—¢ as
<br />C =�ar
<br />A, a
<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 />cog A.
<br />A, c
<br />B, a, b
<br />B = 90°—A, a = c sin A, b = e cos A.,
<br />Solution of Oblique Triangles
<br />Given
<br />A J)—,-
<br />Required
<br />b, c, C
<br />b = a sin B C _ 180°—(A + B), e — asin C
<br />'
<br />'
<br />sin A sin A
<br />A,a,b
<br />B,e,C
<br />sinB=.beaA,C=180°—(A+B),c=
<br />sin
<br />0. b, C
<br />A, B, e
<br />A+B=180'—C, tan J (A—B)= (a—b) tan (A } B)
<br />a -}- b
<br />a sin C
<br />_
<br />c gin A
<br />C
<br />a+ °,,in
<br />a, b, a
<br />A, B, C
<br />a = -A= `�(J
<br />_
<br />J a J—e
<br />sin 118=� ( a ),C=180°—(A-{-B)
<br />e
<br />a, b, c
<br />Area
<br />g = a+2 +c
<br />A, b, c
<br />Areab
<br />e sin A
<br />area =
<br />2
<br />a= 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 />edsine of the vertical angle. Thus: slope distance =319..4 ft
<br />'From
<br />a�sVs
<br />Vert. angle= 50 101. Table. Page IX. cos 5010'=
<br />$1 oQe
<br />ti 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />Horizontal distance also=Slone distance minus slope
<br />Ao�1e
<br />e
<br />a 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 5° 10'=.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=3028 it.
<br />Horizontal distance=302.6— 14 X 14 _3M6-0.32=302 28ft.
<br />2 X 3026
<br />MADE IN U. S. A.
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<br />A
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