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4, <br /> -"TRIGONOMETRIC FORMULIE a / <br /> 7 <br /> 1 i <br /> .Sn C � b C <br /> riangle Oblique Triangles <br /> ' Solution of Right Triangles <br /> 7, , 7 /GoL a b a b a a <br /> For A ,. sin = C ,cos= o ,tan= b,cot =a,sec= b,.cosec= a <br /> Given Required , <br /> oa' 1_ �.a ' a,b, t A, B,a tanA=b= cotB,a = a2 = a 1 i <br /> 2 s <br /> .'-. _ _ <br /> a� � A, B, b sin A=o =cos B,b=%/(a-I-a)(a—'a) =a <br /> 7/� a <br /> �=B, b, o B=90°—A,b =a cotA,c= <br /> sin A. <br /> L! 3 A, k ' B,a, a B=90°—A,a = b tan A,o= b � � <br /> _.. �.. cos A. <br /> d` B, a, b B=900—A,a =c sin A,b=a cos A, <br /> Solution of Oblique Triangles <br /> Required b B 180° ( f a sin U / 9 <br /> : <br /> Yr Z b' °' sinA ' C= —A B), a= 9J �fy <br /> in A <br /> 3g _ Y z _ C sin B= baa A C= 180°—(A-f-B),c = a sin C 7 <br /> sin A <br /> A,B, a A+B=180°—C,tan z(A-B)=(a—b)tan a(A+&) <br /> 3 7 � IL <br /> � _ asin C a I b <br /> sin <br /> v �_ <br /> � ' B, C s_— ti a+b �a <br /> " sin-A= 5 <br /> 2 2 be '/ 7N <br /> 741 .>,. b� 3 ... sin'B= <br /> I / <br /> _ � a s <br /> a+b+a <br /> area = s s—a s— s—a <br /> a.s I77 2 ( ( y iG,s� <br /> b>� <br /> g bas 75- / <br /> o <br /> b in A <br /> 2 <br /> y �' `_- r a2 ein B sin C/ y <br /> area = 2 sin A 1 '�?i!A$• 0 4 L- <br /> 31 REDUCTION TO HORIzWrAL <br /> --- <br /> a / gtaS� e _ <br /> slmultiplied- <br /> i eb] tle <br /> ee cosine thevrticalangleThusopetance <br /> Vert. angle=50 101. From Table,Page IX.cos b <br /> W�99W Horizontal distance=319.4X.9N9=31&09 fL <br /> s"s Arg1e a'Horizontal distance also=Slope distance minus sloppee <br /> > i e distance times (1—cosine of vertical angle). With..the <br /> same figures as in the preceding example,.the follow- <br /> 9 Horizontal distance lue result is obtained.Cosine b°10'=.9969:1—.9969=.004L <br /> - 31 1=1.31.319.4-1.31=318.09 ft. <br /> 2 When the rise is known,the ntal distance is approximately:—the alp dist- <br /> ance less the square of the rise d by Wee the slave distance. Thus:Xise i4 ft.. <br /> 9...`; slope distance=3029 ft. Hortaoat idistrnas=3019— 4 14=80Lg_A32=3b2.28 ft. <br /> 2 X 302:{ <br /> /,L; - •. - ` s ^ ' MADE IN U.ILA. ♦..,'S <br /> t <br />