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6-3. v,� TRIGONOMETRIC FORMULAE
<br /> B B B
<br /> h•-" 6 c a c c
<br /> a a
<br /> 3S jo ie
<br /> b
<br /> _- C �b C A b C
<br /> . � $igLt Triangle Obliique Triangles
<br /> 1 Solution of Right Triangles
<br /> r For Angle A. sin =¢ b a b c
<br /> c ,cos= tan= b ,cot = —,sec=—, cQgec= e
<br /> Given Required a b a
<br /> ` - - a' b A, B,c tan A=b= cot B,c = a2-♦ 2 =a 1 +
<br /> cos B,b
<br /> B, _
<br /> a=
<br /> i a, c A, B, b sinA=as
<br /> A,a b, c B=90°—A,b=a cotA,c= 02
<br /> a y r 2
<br /> ;In
<br /> A, b B, a, c B=90°—A,a = b tan A,-= b ,—1f c
<br /> cos A.
<br /> A, c B, a, b I B=900—A,a =c sin A,b=c cos A,
<br /> Given Required
<br /> Solution of Oblique Triangles
<br /> a ein B
<br /> L4,Q �o A, B,a b, e, a b= sinA ' C= 180°—(A+B),e=asin C
<br /> sin A
<br /> CA, a, b B, c, C sin B=b sin A
<br /> a � = 180°—(A-p.B),a = a sin a.
<br /> sin A
<br /> a, b, C A, B, a A+B=180°—C,tan%(A—B)=(a—b)tan}(A+B).
<br /> `� �z°✓1S �G( - asin C a+ b ,
<br /> C ' sin A.
<br /> .�1OfA a, b, c A, B, C
<br /> sin A�
<br /> .2.
<br /> be '
<br /> .1 sin g— I(s—ao
<br /> a c ,C=180°—(A+B)
<br /> a, b, c Area s_2+b+0
<br /> , area
<br /> 2 = s(s—a a— s—e
<br /> �\ A, b, c Area area =:b c sin-4
<br /> 2
<br /> a4 sin B sin C
<br /> rj A,B,C,a Area area = 2 ein
<br /> ((� REDUCTION TO HORIZONTAL
<br /> Horizontal distance-Slope distance multiplied by the
<br /> 5�o4e a�sce aa cosine of the vertieatangle.Thus:3lQVe
<br /> distanc
<br /> Oft ftaQVert. Ruffle=b°1N. Fro*Table,race Icosb" orHorizontaldistan f4X.98*_31&09 itAole a rizontal
<br /> distance also=slope-di .
<br /> tle tanee times(1—cosine of vartiold#m fIth the
<br /> Pme figured.as in the pt'eeedhit example,the follow-
<br /> Horizontal distance I+is•resalt.is bibMsined.Coaigtb°1d=.99Bi 1°=c911�=D041.
<br /> When the rise is kno X&O(M41=1.31.319.4-1.31=31&O9 it
<br /> wn,flee horizontal distance is approximately:—the elope dist-
<br /> anoe less the square o1 the fl divided by twice the slope distance. Thus:rise=14 ft.,
<br /> _ .. slope distance=3028 ft. Horizostel
<br /> c
<br /> ME IN U." '
<br /> r
<br />
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