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<br />---TRIGONOMETRIC" FORIVIULrE._,
<br />_. B 8;:: B
<br />c a c T, j a c Ic Ab -"Cd 6CA b �
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<br />Right Triangle Oblique Triangles
<br />I Solution of Right Triangles
<br />I For Angle A. sin = , cos= , tan= L. , cot = a , sec.= �, cosec =
<br />Given Required a '
<br />•. ii ( a, b A, B ,c tan A = L = cot B, c = -0/ ' -771 = a IT a x
<br />i { e
<br />f 2, c '4-1?, b sin A = 0 = cos B, b = �/ (c+a) (c—a) = c 1
<br />A, a B, b, c B=90°—A, b = acotA, c= a -
<br />sin A.
<br />A, b B, a, c - B = 90°—A, a = b tan A, c = b
<br />cos A.
<br />4 A, c B, a, b I B=90°—A, a = csinA, b= ccosA, ^
<br />Solution of Oblique Triangles J
<br />Given Required a sin B
<br />A, B, a b, e, b sin A , C = 180°—(A -} B), c = sin A
<br />b sin A a sin'(,'
<br />A, a, b P,, c; C `sin B= a ,C = 180°—(A -f- B),.c = sin A
<br />a, b, C A, B, c A+B-180°— C, tan 1(A—B)= (a—b) cavi 1_(AL+B)�
<br />a -I- b
<br />_asin C
<br />c .sin Ati
<br />a, b, c A, B, C s=a+2+c''Sin 1A= YIs ale
<br />1�ac —i-
<br />aI-b{c
<br />a, b, c Area 8= ,area = (s-21)
<br />A, b, c iAi•eab c sin A
<br />area = 2
<br />A, B, C, a ;Area area = a'- sin B sin C
<br />2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />e cosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />tat<6 Vert. angle=5010'. From Table, Page IX. cos 50 ]0'=
<br />aye 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />$11o1p
<br />c Angle Horizontal distance also=Slope distance minus slope
<br />Ve-t• distance times (1—cosine of vertical angle). With the
<br />same figures as in the preceding example, the follow -
<br />horizontal distance ing result is obtained. Cosine 51101=.9959, I—•9959=.00.11.
<br />319.4X.00-11=1.31.319.4-1.31=318.09ft. -
<br />When the rise is known, the horizontal distance is approximately:—the slope dist-
<br />ante less the square of the rise divided by twice the slope distance. Thus: rise=14 it•,
<br />i slope distance=302.6 ft. Horizontal distance=302.6— 14 X 14 _302.6—o.32=302.28 ft.
<br />2 X302.6
<br />. - • MADE IN U. S.A.
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