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37-9-f _ - ? TRIGONOMETRIC C~ORIv1UL1E
<br />i^..b C A b C A b Gr
<br />i•
<br />Rghi—Trinstgfe-' - Oblique Triangles
<br />Solutiori' of Right•, Triangles '
<br />b a
<br />ForAngle A. sin = — , cos =—,tan= , cot = , sec = cosec =
<br />r jf y . �✓ v �l ire ( ! r . _f. 3 �' % Given. Required E C a. bz a
<br />� % ,a t: d,.li. 1, 73 ,c tanA=b=cot la, ,c= �i' { b -=a 1-f o
<br />�� `�� d rtf73 a, c A, A b sink==cosi,r—\/Toal(G—a)=o�1-0as
<br />-
<br />• , ; • , g, a;- . B, b, c .8=90°—.4, b = a cot -A, c= ¢
<br />�_'' r� ' 2- /l sin A. 3 "'V
<br />k' 2—C o j r/ 'fr-3,6 A b I3, a, e B=90�—A,a btanA,r,=
<br />cos A. d, 6, B, a, b I3 = 90°—A, a = a sin d , b = c cos A,
<br />Solution of Oblique "Triangles
<br />Given Required a sin B a sin C
<br />} r P `Z _ . {e �. ! Y� 1 . • r b = C = 1r:10°—(A + B) r
<br />,`�� 467 f A>.. a b c sin A sin A
<br />_2� fr. • 3 ,_ '�.. b sin d a sin C
<br />G'
<br />/ c D 3 - rr A, a, b Z1 c, C sin R = a , = 180°—(d -f B) r e — sin d
<br />1?(
<br />• $' o J�W. +�)
<br />e / a, b, C A, It, c. ' A 8=180°—C,ta.a z{A—B)- ,
<br />o.00 :) / a sin C a + �a
<br />sin _i 1 �'!• w
<br />G 1i a+b-F e , Jle b)fse) i ti
<br />J
<br />b, c A, B, C a= 2 ,sinzd=` -- b c
<br />L �'3i)//% i .a sin ism. f�'"
<br />ac
<br />':•p �. 3 i .t' IO a, b, —1,
<br />I Area s=a+2+c, (.s—c)
<br />T
<br />besin A
<br />:c' " Area area =
<br />fffff a � e l n i5' si n. G' _
<br />9 �g 7S'• 7 Pty ,'�i A,8, � a Area area =
<br />� 5 ' �., r, 2 sift A
<br />5 c7 . / Z b' _ J REDUCTION TO 11�?RIZONTAL
<br />Horizontal distaa-me Slope distance multiplied by the
<br />cosineof the vertical angle. Thus: slope distance =319.4ft.
<br />Vert. angle =4° ]0''. From Table, Page IX. cos 5° 10'=
<br />//J e bis y 9959. Horizontal distance=319.4X.9959318.09 ft.
<br />ogle Horizontal distan-ce also=Slone distance minus slope
<br />distance times 11 --cosine of vertical angle). With the
<br />same figures as in the preceding example, the follow-
<br />' 4 Z ing result i s obtained- Cosine 5° 10'=.9959.1—.9959=.0041.
<br />Horizontal distance 319.4X.0041=1.31. 5 9.4-1.31-319.69 ft.
<br />When the rise is known, the horizontal distance is approximately:—the slope dist-
<br />`/t fir— ,J ante less the square of the rise divided by twicrethe slope distance. Thus: rise =l4It..
<br />/ 14
<br />� / slope distance=302.6 it. Horizontal distance=10 6—� 506 302.6-0.32=302.28 ft.
<br />c - ( MADE IN U. % A.
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