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TRI6H31 0bMTRIC FORMULA
<br /> I ,_ Z _ B B B
<br /> Xx .�- 6 x -t C _ C)
<br /> a a o
<br /> C
<br /> C b C A 6-
<br /> � Oblique Triangles---1
<br /> r 7 7 Solution .of Right Triangles
<br /> 0 �7 /-Z Fare n =o,cos= a a-.
<br /> ,.cot- a,sec- b,cosec - .a
<br /> 4 �4
<br /> '4f► ,o tan A=b= cot B,c=��= a 17 as
<br /> b sin A- =coo B,b=,Vo-i-a a--•a =o V 1
<br /> 02
<br /> 13
<br /> A a & a B=90°-A,b = a cotA,a= a .
<br /> --- 1 ,
<br /> sin A.
<br /> o . B=90°-A,a = b tan A,o= b
<br /> _ - — . cos A.
<br /> A,a B,a, b B 90°--A,a =o sin A,b=a cos A,
<br /> Solution of Oblique Triangles
<br /> Given Required
<br /> d, B,a b, a, C b= sin , C= 180°—(A+B), 0 = asinC
<br /> sin A
<br /> _ b sin A
<br /> 7 6 7) •J1,c, C sin B= ,C= 180'-(A+B),c = a sin C
<br /> a
<br /> ^ I sin A
<br /> A,B,a A+B=180°-.C,tan J(A-B)= a-b tan k(A+B)
<br /> a sin C
<br /> zi4n ` a + b '
<br /> ,,,, ..�. _
<br /> 'V ( Flo we a sin A
<br /> ,;,7 V a+ +Gti � , d, B, C a- ,Sin JA=.19=9—e
<br /> a Z bo
<br /> -j _ sinjB�- �a-a)a(c, C=180°-(A+B)
<br /> _a+b+
<br /> oa / a, b, a #res, a_ 2 �, area = e(a-a F,,
<br /> A, b, c 1zea area = b a eiii A
<br /> �1 t 2
<br /> ,3 '00142 ein B gin C
<br /> A,B,'C,a 'area, area = 2 sin A
<br /> REbuCTION TO HORIZONTAL
<br /> -� Horizontal distance=Slopq distance multiplied by the
<br /> e cosine of the vertical angle.Thus:slope distance=s19.4 it,
<br /> I c Vert. angle 50 101. From Table,Page IX.cos b°�II1W-
<br /> 9989. Horizontal distance=319:4X.9969=818.09 ft.o0e �at�e Horizontal distance also=Slope distance minus I slope�e distance times (1—cosine of vertical angle). With the '
<br /> same figures as in-the.preceding example,the follow-
<br /> Horizontal distance Inc result is obtained.Cosine 60 101=.0869.1—. =.0041.
<br /> 819.4X.0041=1.31.919.4-1.31=318.09 ft.
<br /> When the rise is known,the horizontal distance is approximate)y—the slope dist-
<br /> ance less the square of the rise divided by twice.the slov"Istanee. Thus:rise=14 ft.
<br /> 'slope distitace=802 8 ft Horizontal distance- OLO—14 X 14=802.8-0J2--=3 b28 ft.
<br /> _.: 2 X-801e
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