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9 �d rf,Yri ��v
<br /> ✓•I0~ - TRIGONOMETRIC FORMULtE
<br /> B
<br /> a
<br /> A - C `•
<br /> 3.. /,r 71. ?. % Right.Triangle Oblique Triangles
<br /> f Solution of Right Triangles
<br /> For Angle A. sin =a epe= b tan= a b e e
<br /> �d /�B�7S�i✓ w c , c , b E'Cot = a,see= b, cosec = a
<br /> Liven Required I 2
<br /> b A, B,c tan A=a a 2-{- 2
<br /> cot B c = a = a 1 { —
<br /> G;:s;�a
<br /> a, e' A, B, b sin A= a =cos B,b=,Vc+a c--a)=c 1—a2
<br /> l} J A,a B, b. c B=90°-A,b =acotA,.o= a
<br /> _. sin A. 1
<br /> f' x A, b B,a, a B=90°-A,a = b tan A,c= b
<br /> cos A.
<br /> A, a B,a, b B=90°-A,a =c sin A,b e cos A,
<br /> jS ) Solution of Oblique Triangles
<br /> � r � � / � d '7� Given Required _ a sin B
<br /> ' v � /'1 A, B,a b, c, C b b: A ', C = 180°—(A+B),c= sin A
<br /> in
<br /> — b sin A ° -sin C
<br /> A, a, b B, c, C s n B- ,.0= 180 -(A-t-B),c =
<br /> -7 3 1 a sin A
<br /> a, b, C A, B, c A+B=180°-C,tan n(A-B)-(a-b)tan J(AA+
<br /> 0 (s _ asin C
<br /> L d sin A
<br /> b G v;, c — s r 1 Y a
<br /> GJ5 ) 3 � �5f 1t / t6� �.�r
<br /> �� Z; i b, a A, B, C a-a+Z c,sin'',A=�('I b(C-c)
<br /> r
<br /> sin zB-1�(s-aa a C-180°-(
<br /> v
<br /> +B
<br /> r --
<br /> a 33 a, b, a Area 8=a+b+0.
<br /> 2 , area =V.(7 TC.- s-c
<br /> , e Area b e sin A
<br /> A, b
<br /> ' area = 2
<br /> ' 14a2 sin B sin C
<br /> are
<br /> a =
<br /> 2_
<br /> A,B,C,a Area
<br /> snA
<br /> REDUCTION TO HORIZONTAL
<br /> Horizontal distance—Slope distance multiplied by the
<br /> .. Z . ce cosine of the vertical angle.Thus:slope distance=319.4 ft.
<br /> 7 �9taQ Vert. able=5°10,. From Table,Page IX.cog 5o 10'=
<br /> 8969 Itorizontal distance=319. X-9969-11MO9 ft.
<br /> j. S�O� Ap4�e Horizo distance also=Slope distance minus slope
<br /> �, Ve distance times (1—cosine of vertical ang%). With the
<br /> // same 1t4vres as in the prece$ine example,the toiiow-
<br /> Horizontal distance ing result is obtained Cosine 5°10,®.8868.1—.9869=.004I.
<br /> i 818.4X.6041=1.51.819.4-1.81=01LOO ft.
<br /> i When the rise is known,the horizontal distance is aPProximately:-the slope dist-
<br /> rise leas the square et the rise divided by twice the eloPp M,Than;rtse=14 M.
<br /> slo
<br /> De dfataaoe-79a$!t alr+69g6— +50®6-b0 .it,
<br /> 2 X 9026 ,
<br /> MADE IN U.S.M
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