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k 7-_41 7 ` V TRIGONOMETRIC FORMUL F,
<br /> r .
<br /> 3R B B B
<br /> 7 ani v 3�P - a a c a a a
<br /> / 0 7.47 3 /� b C A b C A b C
<br /> Right Tre Oblique Triangles
<br /> Solution of Right Triangles
<br /> a b a b a c
<br /> e,, r -
<br /> 3 Y.S w For Angle A ;in = a coo= o tan= b ,cot = a,sec= b, cosec=
<br /> �;
<br /> ' „. a
<br /> 7 N Given lied a
<br /> 3. a, b �, ,c tanA= b= cotB,c = az+ 2 = a 1 + a2.
<br /> )- G o ayy
<br /> /v9. .73 �_— ---
<br /> C1 9 3 +t £ 7 a 3 Ja b.z y 3 7 7. I D ' a
<br /> / 7. ./ 6 9 3 3 a, c A, B,
<br /> B� b sin A=—=cos B,b=V(c+a)(,---a) =c 1—_
<br /> 1
<br /> 4 / 9, 0 1 ~?s A,os �, b, a B=90°—A,b =a cotA,c= sin A.
<br /> y L 7 j y
<br /> 39 '� _j _ rrsa B,a, 0 B=90'—A,a = b tan A,c= b
<br /> 1 _
<br /> J J 3.z L `� /.°3 0 / a 9 ' a ° cos A.
<br /> r 3G Jv/. j. 3 yG8 ) 9/ A,o �B,a, b B=90 —A,a=csin A,b= ccos A,
<br /> o / / S L/ / 91' c o 3 3 Solution of Oblique Triangles
<br /> f /v9 -C9 / 3, f / $ red
<br /> ?,"8 _y ' 3 L d $i ' mac C b =a ein B C= 180°—(A+B), c = a sin C
<br /> /o�� ,, i i i•o y G G 1 /•3 3 L l 7.'s n•4*19 sin A ' sin A
<br /> b sin A a sin C
<br /> e l 7 -- C sin B= ,C= 1800—(A+B),a =
<br /> 7 7 °� 9s 3.7 9j /v/ 13 * a sinA
<br /> 1° 3't j / a—b)tan 1(A+B)
<br /> j 3 If G /o o G y 3 f n , ,a A�B-180 C,tan (A—B)= a 6 +
<br /> _.033 , 3; /a-7: 7 7 ° sinA
<br /> 3 f / 9 37 L ) 3 J D�'7 ,,I
<br /> 7r / s9 °y / 2FP b, o A, B, x=a+ sinlA=Vlx br�—c ,
<br /> 9. 7'17 /by,6 l Z
<br /> /a6 9 S 3 / 3- /'_. / 3 3 7� d " sin�}B=J(x—axx—c ,C=180°—(A+B)
<br /> a' .t ac
<br /> 7 , 3 Jnd� y , a+b a
<br /> 7 9 9 a,' b e Agee x= 2 , area = s(s—a)(s--b) a�
<br /> y 3 /d3P� A, b e ltsa bosin A
<br /> O
<br /> 3 z 3 3 , area = 2
<br /> 363 �� " r �o/ S3 A,B,Ca Aa2 sinBsin 0
<br /> , ea area a 2 sin A
<br /> •,�c 9 � �� � 3 REDUCTION TO HORIZONTAL;
<br /> Horizontal distance=Slope distance multiplied by the
<br /> /°p s 3 _ o ? 7 3 / 3 cosine ofthe vertical angle.Thus:slope distance=319.4 ft
<br /> tspde Vert. angle=6°101. From Ta�,Page lX.cos b°ld=
<br /> --- s. ry } ),! �} o4e ays .9D59 Horuontal dlstanee=s19 s5C.9 o—N&OD ft.
<br /> 21 (�8 $1pg1e Horiaontai distance also=Slope distance minus slope
<br /> ti a- _ 3 G distance times.(1—cosine of vertical angle). With the
<br /> _r JN gy / y,7 f_ J v` y Vc same figures as in the preceding eXample the follow-
<br /> Horizontal distance lag resoit U obtained.Cosine 6 lli'=.99M 1-00=.0041.
<br /> ° a When the rise is known,t4a IsX'0s�1 dis slta bee h sapgroox msiety the elope dist-
<br /> y aAce less the square of the risY divided by twice the skee distadoe.. Thus rise=l4 ft.,
<br /> slope distance=802.9 ft Horlmatal distaues-802E--mi=l—80&6-e42-3O.28 ft.
<br /> ZX 802.8
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