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'All a /.,, oe_ iT 5 A4AI . I . 151/
<br />TRIGONOMETRIC FORMULAE
<br />B B B
<br />a ca a
<br />N
<br />C At b C A b C
<br />Right Triangl; Oblique Triangles
<br />Solution of Right Triangles
<br />-For Angle A. sin = Dcos = @ tan = cot = a , sec cosec = a
<br />Given Required
<br />a b A, B,c tan A cot B, oc N/ -a-2—+72 +
<br />b + 7a,
<br />7-2
<br />a, e. A, B, b sinA=2�=cos B,b=\1(a+a)(r_—a)=c 1— a —
<br />. a 02
<br />A, a B, -b,. o B=90°—A, b= a cotA, o= a
<br />sin A.
<br />A, b B, a, c B = 90'=A, a. = b tan A, c = b
<br />cos.A.
<br />A, c. B, a, b B = 90*—A, a = c sin A,b,_cos
<br />Solution of Oblique Triangles
<br />Given Required b = asin B, asin C
<br />A, B, a b, o, C C = 180*—(A + B) , c
<br />sin A sin A
<br />b sin AC = 180'—'(A + B), c = a -sin C
<br />sin ,
<br />A, a, b B, c, C a sin A
<br />(A
<br />b, C A, B, o A+B=180*— C, tan I —B)=
<br />(a—b) tan 1, (A+B)
<br />a sin 0 a+ b -
<br />sin A
<br />a, b, a A, B, C=a+b+ "in',A=-V 1 b
<br />2
<br />sin ,'B= -\l a c 0=1$0'--(A+B)
<br />b
<br />a, b, o Area 8=a+2+area = Nls(8 aTT8 s
<br />A, b, e Area area = b c sin A
<br />2
<br />a' sin B sin C
<br />A, B, 0, a Area area = 2 sin A
<br />REDUCTION TO.HORIZONTAL
<br />Horizontal distance =Slope distance multiplied by the
<br />'Ce cosine of the vertical 29110nh us: slope distance =319.4 ft.
<br />Vert. angle =50 101. From Table, Page IX. cos 50 10/=
<br />e 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />61�:10
<br />Horizontal distance also�Slope distance minus slope
<br />I ve� Ie-
<br />P",%*e 'distance times (1—cosine of vertical angle). With the
<br />e. same figures as in the Preceding example, the follow-
<br />ing result is obtained. Cosine 50 101=.9959.1—:9959=.0041. �
<br />Horizontal distance 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=302.6 ft. Horizontal distance=302.6— 14 X 14 =302.6-0.32=302.28 ft.
<br />2 X 302.6
<br />WE W U. 46&
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