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<br /> b S, 0 F�-�► ! F o 0 0.6 I
<br /> /T NO#ETRIC FORMULlE j
<br /> J <, B
<br /> 4. 4
<br /> a c a/�' 73 c
<br /> y a
<br /> At b a A c
<br /> z 7 Right Triangle Oblique Triangles nB
<br /> 3 •y ! f - Solution of Right Triangles
<br /> ?
<br /> g 8
<br /> = 7 — o 3 g For Angle A. sin =c,cos= ,tsa= b,cot Q,sec=Tp cosec=
<br /> .G ! r� �/ 1 Given Required a a
<br /> t
<br /> o� �/ _ a �, `,' 7 a, b A, B,c tan A=b= cot B.a= a2 ♦ $ _.a 11-�
<br /> I V` _
<br /> a, c A, B, b sin A=o=cos B,b=V(a+a (o—a =c F. a
<br /> J _ a B b c B=90°-A,b =acotA,a= a o
<br /> s
<br /> sin A. a/ r�T
<br /> f' 3
<br /> , b B,a> a B=90°—A,a = b taa A,c= b
<br /> `y con A Zj" f
<br /> A,c B, a, b B=90°—A a =c sin A b=a cos A,
<br /> �' `,`� . ;34 3 3 Solution of Oblique Triangles
<br /> l 3'4 c Given Required a sin B
<br /> A, B,a b, c, C b= , C= 180°:—(A+B),e= a sin C
<br /> sin A sin A
<br /> - A, a, b B, c, C sin B= b sin A r C= 180°—A _ a sin C
<br /> 1 a ( tB),a —
<br /> Ld 9 sin A
<br /> a, b, C A, A c A+B=180°-C,tan a(A-B)- a-b)tan (A+B)
<br /> asi a+ b
<br /> n A .
<br /> si �
<br /> _--- / a, b, a A, B, C s=a+2+a,sin#A=V a xa—c V
<br /> t '
<br /> V bo , z.
<br /> c t --- sinzBzRN c ,C=180 A B
<br /> vV °—( t )
<br /> a, b, c Area a a+b+
<br /> = 2 , area = a s—a s— )(a—c
<br /> i
<br /> b e sin A avr r
<br /> -..- --- " , a Area s
<br /> y A b
<br /> --.�.. area = `°�0
<br /> J�
<br /> a2 sin B sin C
<br /> A,B,C,a Area area = ----- Y..
<br /> Y•���`� : j-..� -:-_.,._-.. �� �,:� y.�- 2 sin A
<br /> REDUCTION TO HORIZONTAL
<br /> Horizontaldistance=Slope distance multiplied by the
<br /> d
<br /> _ cY ce cosine of the vertical angle.Thu:slope distance=819.4 ft.
<br /> ' `• / �' a a�stp� aHorizontalN. From Table.Page IX.cos 5610,=
<br /> 5104 Argue A Horizontal'distanceso 1&4X.9869=M&09 ft
<br /> distance times Slope distance minus slope
<br /> I 1? ^f Qe (1—cosine of vertical angle). With the
<br /> same figures as in the preceding example,the follow-
<br /> 1 4, , Horizontal distance ing result is obtained.Cosine ti°fo,=.8969.1—JM=-0041.
<br /> —� --e- X&4xM&l=1.3i.819.4—l-K--t1&09fL
<br /> When the rise is known,they
<br /> ante less the square of the riseilieldeel IIbe is�oximately- the slope dist-
<br /> ance twrbe the slope distance. Thus:rise=14 ft..
<br /> --— slope distance=4p2 O ft Horizdltal distaae,.j6.— X It—3MG&32=SX28 ft.
<br /> Me
<br /> ci
<br /> 40' % ,MADE al U.S.A.
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