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T eT TRIGONOMETRIC FORMULAE
<br /> B B J3,
<br /> 7 B
<br /> -- c c a c
<br /> 77 63 J 9a
<br /> 3
<br /> 2/7 C b: . b C A c
<br /> b
<br /> _ J
<br /> ' l �: � � �f P "` ,Right Triangle Oblique Triangles
<br /> y7 ' �,s . Solution of Right Triangles
<br /> . � _ $ '? ✓.. ,c For Angle A. sin =o ,cos= b,tan= b a;cot = b sec= cosec e
<br /> ' c a b. =
<br /> 3 St �/ Given Required a a
<br /> 3 ! r J 3 +� a, b A, B,c tan A=b= cot B,c = a2-{ l = a 1 E 2
<br /> (o Cl a a
<br /> r / ) c A, B:`,b' sin A=c=cos B,b= (c-I a)(c—u) =c J 1—a
<br /> �3 G = '
<br /> _... _ a
<br /> o
<br /> . S 3 A,a �Y, b, c B=901L—A,b =a cotA,c=
<br /> sin A.
<br /> A, b B,a, c B=90°—A,a = b tan A,c= L12�-
<br /> cos A.
<br /> A, c B, a, b B=90°—A,a=c sin A,b= c cos A,
<br /> /S - / / Solution of Oblique Triangles
<br /> e �--- —� Given Required 4 a sin B B, a b, e, _C b '
<br /> sin Ac
<br /> C= 180°—(A+B), — a sin C
<br /> sin A
<br /> sin A
<br /> + td 70 �O A, a, b B, c, C sin B= a ,C= 180°—(A+B),c = a sin C
<br /> sin A �
<br /> } ',� � �S 7 a, b, C A, B, c A B-180°—C tan- A—B _ a�)tan ♦(A B)
<br /> �- 5L I �--' �,� j7 of a sin C +
<br /> c —7--
<br /> sinA
<br /> wy
<br /> � 71 _ '= a, b, c A, B, C a=a+b+c,sin'A= V(s=bCs—c
<br /> � 2 be '
<br /> sin zB= a a ),C=180°—(A+B)
<br /> _ / a+b+c
<br /> / b, c Area S=— , area = a s—a s— s—c
<br /> � ) 2! v A,,b, c Area b e sin A 7 j 4-
<br /> area =
<br /> /.,; ? G
<br /> T• .3� �',�tr ___..�-%� ^; ✓ a2 sin B sin C 3 � t� 5•ti
<br /> -_ A,B,C,a Area area = 2 sin A l
<br /> ►"" REDUCTION TO HORIZON o
<br /> i Horizontal distance=Slo i nc+e multiplied by the
<br /> T cosine of the vertical angleus!slope distance=319.4 ft.
<br /> Stanpe Vert. angle=51101. From Table,Page IX.cos 5°10'=
<br /> -5 4• r / S�O� pale H Horizonta9. l distance zontal salsoe Slope diistance minus slope
<br /> R �e A a distance times (1—cosine of vertical angle). With the
<br /> 4 same figures as in the preceding example,the follow-
<br /> Horizontal a Horizontal distance ing result is obtained.Cosine 5°101=.9959.1—.9959=.0041.
<br /> - 7 r ` _` - 319.4X.0041=1.31.319.4-1.31=318.09 ft.
<br /> When the rise is known,the bo n''ggontal distance is approximately:—the slope dist-
<br /> Ji J } sues less the square of the rise divid6d by twice the slope distance. Thus:rise=14 ft.,
<br /> ' = slope distance=302.6 ft. Horizontal distanoe=3026—!# 14 I 2X302.8=3026-0.32=30228 f.
<br /> MADE IN U.B.A.
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