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TRIGONOMETRIC FORMULA
<br /> B B B
<br /> a ° e
<br /> a a
<br /> 7$
<br /> -- b C A bC A b
<br /> C
<br /> o ' Right Triangle Oblique Triangles
<br /> I'
<br /> I o Solution of Right Triangles
<br /> a
<br /> For Angle A. min =a ,coo=
<br /> Q,tan= b ,cot = a b, cosec=
<br /> 6
<br /> Given Required
<br /> -- ,c� , a, b A, B,o tan A=b= cotB,a = ash s = a 1
<br /> 4 o a, a A, B, b' sin A=a =cos B.b= a a c—a =e —1—EL
<br /> C
<br /> 02
<br /> J A,a B, b, c B=90°—A b =a cotA a= a
<br /> ' sin A.
<br /> A, b B,a, e B=90°—A,a = b tan A,c= b
<br /> z 3 cos A.
<br /> A,a B, a, b I B=90°—A,a=c sin A,b=e cos A,
<br /> t 9 Al Solution of Oblique Triangles
<br /> / Given Required a sin B
<br /> d, B,a b, e, C b = in A ' C= 180°—(A+B), e ='gin C
<br /> s
<br /> sin A
<br /> b gin A
<br /> A, a, b B, c, C sin B= a ,C= 180°—(A-i-B),o = a sin C
<br /> sin A
<br /> a, b, C A, B, a A+B=1800—C,tan;(A—B)—(a—b)tan 1(A+B)
<br /> a+ b ,
<br /> c =
<br /> a sin C
<br /> sin A
<br /> a, b, a A, B, C 8=a+2+a 'in jA=N18 be
<br /> sin zB=V 8�a a ,C=180°—(A+B)
<br /> a�-b-�c
<br /> a,'b, a Area a= 2 , area
<br /> A, b, e, Areab c sin A
<br /> area = 2
<br /> area =as sin B sin C
<br /> A,B,C,a Area
<br /> 2 sin A
<br /> REDUCTION TO HORIZONTAL
<br /> Horizontal distance—Slope distance multiplied by the
<br /> ice cosineottheve roh'cal angle.Thus:slope distance=319.4tt.
<br /> Vert angle=6 10'. From Table,Page IX.cos bo lw=
<br /> o0eo Nis
<br /> Horizontal distance=319.4X.9960=318.09 it.
<br /> le Horlsontai distance ah—Slope distance minus slope
<br /> Apa
<br /> distance tinea fit—cosine of vertical angle). With the
<br /> same figures as in the preceding example,the follow-
<br /> Horizontal distance ing result is obtained.Cosine 60 lof—.9951L 1—.9m-.0o4L
<br /> 819.4X.0041=1.31.319.4-1.31=31&0o ft
<br /> When the rise is known,the horisantad distance is approximately:—the slope dist-
<br /> anee less the square of the rine divided by twice the slope distance. Thus:rise=l4 tt,
<br /> slope distance=302.6 ft HorizonW distsnge-3M&-..1 X Z4:3DL6—p,3y=902,28 g,
<br /> 2 X 302.6
<br /> MADE IN U.S.A.
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