|
Cf ��
<br /> 9; �•8 a �YRIGONOMETRIC FORMULAE j
<br /> a a a a 7 a
<br /> C
<br /> ? b a A�6 C b
<br /> Right Triangle Oblique Triangles
<br /> Solution of Right Tsianglea
<br /> g 1 g a b _ a b sec=6, cosec= a
<br /> For Angle A. sin = ,cos= a .tan _b ,cot = a, b a
<br /> Given Required a
<br /> / �./ 5 7 a, b A, B,c tan A= b= cot B,c aE+ =a 1 77.
<br /> — 71
<br /> y s
<br /> ? 7 1$ `_ a, o A, B, b sinA=Q=cosB,b=-,/ c+a --a =c 1—oT
<br /> •� 1. 3 1 y` a
<br /> 6 "' -jr
<br /> U_ b J A,a B, b, c B=90°—A,b =a cotA,a= sin A.
<br /> ~ I �
<br /> r � i B=90°—A,a = b tan A,c=
<br /> '
<br /> c A, b B,a, a cos A.
<br /> / 9 A,a B, a, b I B=90°—A,a=c sin A,b=a cos A,
<br /> a Solution of Oblique Triangles
<br /> Given Required a sin B a sin C
<br /> / b = , C= 180°-(A+B), a =
<br /> l0 7 S �'/ A, B,a b> a, L' stn A sin A
<br /> f•'o / Y _ „ bsinAasin C
<br /> A, a, b B, c, C sin B= a ,C= 180°—(A+B),e = sin A
<br /> (a—b)tan z(A+B)
<br /> b, C A,B,c A+B=180°—C,tan a(A—B) a b
<br /> _asin C ++
<br /> 9 _ •.�"�_. f-- a ein A
<br /> I s-.
<br /> a, b, c A, B, C a=a+2+a,sin'-, A=Ali" b a—a , g
<br /> ____.—._- _. /1 / • / /� L sin-B=J(s—aa c ,C=180°—(A+B)
<br /> Area 8=a+2+a, area = e(a—a s— (s—c
<br /> b o sin A
<br /> A, b, c Area area =
<br /> 2
<br /> "i r A,B,C,a Area area =as sin B sin C2 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 /> Vert angle=5°1W. From Table,Page I&cos 5°10'=
<br /> 1 r aisle d 9969. Horizontal&stanos=319.4X.9969-91&09 ft.
<br /> 5,00e ,o%e a Horizontal
<br /> utaaae timea�(1-cosine of Slope
<br /> anglance e minus
<br /> 3 J / ve same figures as in the preceding example,the follow-
<br /> Horizontal_ distance ing result is obtained.Cosine 6°1W=.9958.1—.8859=•0041.
<br /> 819.4X.0641=1.31.3194-1.31=51&08 ft
<br /> When the rise is knowthe borhmatal distame is approximately:-0
<br /> s, e slope dist-
<br /> / i ante less the square of the rise divided by twice the slope distance. Thus:rise=l4 ft,
<br /> slope distance-3026 ft Horizontal distsaes=30LO-2 X 862.614 X 14=302.9-0.52=302.28 ft
<br /> ±'� 3 J - - MADE IN Y.6.A.
<br />
|