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<br /> - 3 l TRIGONOMETRIC •FORMULfE G
<br /> �� & l c 1�' � �c G97
<br /> 0.Z �� 4 a �.SZ. a
<br /> - V i
<br /> C d�b. C A b C
<br /> �r Right T1�ingle Oblique Triangles
<br /> `. Solutiop of Right Triangles
<br /> a b a b
<br /> c - -For Angle A,-' in = o ,cos= o ,tan= b ,cot = a,sec =b, cosec= e
<br /> Given PAWAred a
<br /> a, b Ax`B,c tan A=b= cot B,c = a2+ 2 = a 1+
<br /> TEa
<br /> _�-
<br /> 5 � /a � a, o A,.B, b sinA=a=cos B,b=Vo+a o� =ol—a=
<br /> v C ��
<br /> A,a B, b, o B=90°—A,b =acot A,a= sin A.4\ Z l7` /.-7
<br /> dk " �� A, b B, a, e B=90°—A,a- b tan A,o= b
<br /> q3 cos A. s. /
<br /> r � � C� p'J A,o Aa, b B=90°—A;a = asinA,b= ocosA,
<br /> L Solution of Oblique Triangles
<br /> Given Required
<br /> a sin B
<br /> A, B'a b, o' C b sin A ' C= 180°—(A+B),a =sin A
<br /> b sin A
<br /> 2' J 7.3 /pA,-a; b B�/� �j � i�`j � , c, L'' sing= a ,C= 18'0°—(A-i-B),o = sinA
<br /> a, b, 0 -A,B,o A+B=1801—C,tan J(A—B)= a—b)tan a(A-(-B)
<br /> c = asin C a + b ,
<br /> sin
<br /> j)
<br /> } a, b, o A, B, C 8=a+b+D cin'''A= e- )e—c
<br /> D 3.
<br /> ae
<br /> ,C=180°—{A+B)
<br /> aa_
<br /> q a, b, c Area 8= area 2 , = s(s—a s— s—o
<br /> 7besinA
<br /> A, b, c Area area = 2
<br /> ' i 3 a2 sin B sin C
<br /> 1 / / B,C,a Area.- area = 2 sin A
<br /> !, /P REDUCTION TO HORIZONTAL
<br /> Horizontal distance=Slope distance multiplied by the
<br /> Q cosine of the vertical angle.Thus:slopedistance=319.4 ft.
<br /> '7 7 atiytace Vert. angle=b°10'. From Table,Page IX.cos b°10'=
<br /> /
<br /> p e w 9959. Horizontal distance=319.4X.9959=31&09&I t a�0p A�q Horizontal distance also=Slone distance minus slope
<br /> som2 ` e distance times (1—cosine of vertical angle). With the
<br /> Q ins refigures
<br /> ult i obtained Cosine 6°io-.example,the
<br /> .Dog.
<br /> follow-
<br /> Horizontal distance 319.4x,0041=1.31.319.4--1.31=31&o9 ft.
<br /> When the rise is known,the horizontal distance is approximately:—the slope dist-
<br /> e less the square of the rise divided by twice the slope distance. Thus:rise=14 ft.,
<br /> Pe distance-3028 ft. Horizontal distance=3o2&-14 X 14=3026-0.32=302.29 it. "
<br /> 2 X 302.6
<br /> - MADE IN U.\.A.
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