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b° TRIGONOMETRIC•FORS I�d _ {;`
<br /> B B _ B
<br /> TA-
<br /> 1 G -a NK a c a o a
<br /> 7jj
<br /> -T ) o g ` y i a tb �, � b � 1-9 ?9
<br /> 6�F 7.-2, ;;� le Ohlique Viangleg. f+
<br /> 2.0 �.. Solution of Ri=ht"Triangles -Vi p
<br /> in a b a b o d
<br /> s = o ,cos= o ,tan= b ,cot = a,sec= b, cosec = a
<br /> y 6 !liven +lbtlatred
<br /> a,b d,B,e tanA=b= cotB,c =N/752+77 a 1T
<br /> 3, oq w t J'�1. r --� y ��� a, o :,A B, b einA=Q=cow B,b= (e+a c-a) =e 1-a i
<br /> G G yf 7
<br /> f t�' 7-f t! _ A,a B, b, c B=90°-A,b =a cotA,c= a
<br /> 3• L% ) 4 V ,25 7 o�c 2 sin A.
<br /> b7 Tl
<br /> 70 o a k A b - B a o B=90°-A a = btanA o= b
<br /> 3 , 12 14 .31 LG.3/ L �.a b� 03 , , , cos A.
<br /> L �8 y.�s 3 .r� x.ss b�.iy A,o B,a, S B=90°-A,a=osinA,b=ecoaA, 4.i,3 p
<br /> �,f y 3 4 is Solution of Oblique Triangles i
<br /> ` ,f_f (r l 6�• Given Required
<br /> `�• 3 B a sin B
<br /> � o .M 3 o _y �k,1 L (. L A, B, a b, e, C b = sinA ' C= 180 -(� +B),o= s A
<br /> b sin A a sin C
<br /> L 6y J- P L r .�-9 3 ' 5,°a G` 3� . A, a, b B,a, C sinB= a . ,C= 180°-(A-(-B),a = sin
<br /> 4.
<br /> 3 . 4(_J i _ a-b)tan V: B
<br /> a' .? ' _� .,4 aJ a, b, C A, B,o A f B=180°-C,tan;(A-B)- a + b—�, .
<br /> 00 19 v1', °O G� .33 _ asinC
<br /> z- o sin 63.73
<br /> (.T�' .� '.-2�� a+b+c
<br /> 3.7 3'
<br /> &1..3- (66 •� 'L a, b, o A, B, C s 2 ,sin jA=
<br /> 3 `
<br /> 3
<br /> e-a s-c r
<br /> einB=V
<br /> ad �C-180- (A+B)
<br /> .10
<br /> 64 !n_ J . 4 9 c v �- 6q , a+b+a
<br /> 2. 9 �� a, b, o Area a= , area
<br /> 7'P 2
<br /> b7 f � !.y 4 ,Y g i�. 3 t' sem' bcsin A b �.9L 7y,
<br /> y ' ---`_" 3, z.5 L.T .3 � A, b, c Area area = .� ,r 3 7
<br /> 7 3L$ , 18 14 13 t 0"i' s a$sin B An C � `f� v 3 %
<br /> L 2 ?8 �' '.4 A,B,C,a Area area ------ ;
<br /> 3, G 2 sin d_ �- _%w
<br /> c 3' .i"�' 4 REDUCTION TO HORIZONTAL
<br /> b 3 ' `f j o ay y 4 a {b•5 f Horizontal distance-Slope distance multiplied by the '
<br /> 3 , ► �' / ` `( y G`� cosine of the vertical angle.Thus:slope distance=319.4!!
<br /> L v 4,� o Vert. angle=6°ld. From Tripontal able.Page IX cos 60 ld=
<br /> i a a 7 0 i 3 `� (o v � 3 3 ,b ° � ( �� 1,y,4�e � HorizoAM ntall distance also Slope dis�tanceminus slope
<br /> distance banes(4-eosins of vertical angle). With the
<br /> same-figures ss in the preceding exwnpl%the follow- ,
<br /> HoMz*aW disc M Ing result is obtained.Cosine r 10'=.9969.1-.9969=.0041.
<br /> 419AWien file tise is known,the horizontal distan is apo lrozima�y the slope dist-
<br /> L &00 ft
<br /> `/ anos less th9 aquae of the rise divided by twlee the slope distanse, Thus:rise=14 it.,
<br /> S b C 4 7 '7 9 slope di.tama-l9@ s R. BoriSontal dl e-Me-14 x 14
<br /> -I.9-*J2-MZ2B tt.
<br /> M1 4�1 V
<br /> dO
<br /> IV _
<br />
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