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TRIGONOMETRIC FORMUL&
<br /> 8 B B
<br /> J
<br /> a c a c
<br /> L' a
<br /> 4 A
<br /> ... b � /y A�y C, A C
<br /> Right Triangle
<br /> � Oblique Triangle:
<br /> Solution of Right Triangles
<br /> . a a b a b
<br /> For Angle.AL. sin = c ,cos= e ,tan= b,cot = a,sec - bp cosec=
<br /> / j ! Given Required , a
<br /> a, b A, B,o tan A=b= cotB -�c = a2z =a 1+a
<br /> a
<br /> l a,•a A, B, b sin A=c =cos B,b=%/ c a a—a) =a
<br /> / ,=o G s
<br /> aT-
<br /> .A�a B, b, c B=90°—A,b =a cotA,e= a
<br /> sin A.
<br /> �0 A, b B,a, c B'=90°—A,a = b tan A,c= b
<br /> cos A.
<br /> A,c B,a, b I B=90°—A,a =0sin A,b= ccos A,
<br /> Solution of Oblique Triangles
<br /> Given Required a sin B
<br /> A, B,a b, e, C b = G''= 180°—(A+B), e =asinC
<br /> q sin A ,
<br /> sin A
<br /> j" b sin A
<br /> rJ A, a, b B,c, C sin B= ,C= 1800—(A B),a = a sin C
<br /> 1 / a sin A
<br /> a, b, C A,B,e A+B=180°—C,tan 1(A—B)=(a—b)tan a(A+
<br /> 1l �-
<br /> a sin C a+ b ,
<br /> _
<br /> sin A
<br /> a+b+cla_ la_a
<br /> ,a a, b, a A, B, C s= 2 :sin A—
<br /> be '
<br /> sin JB=V(a�a c C-1800—(A+B)
<br /> >
<br /> a, b, c Area s=a+b4-c
<br /> —2 ,area = s s—a s— ) s---c _.
<br /> - A, b, c Areaarea = b e i A.
<br /> tas sin B sin C
<br /> A,B,C,a Area area =
<br /> 2 sin A
<br /> REDUCTION TO HORIZONTAL
<br /> Horizontal distance=Slope distance multiplied by the
<br /> cosine of the vertical angle.Thus:slope distance-319.4 ft.
<br /> eQ�` Vert.angle=b°iw. From Table,Page I%cos t 501w--o .9969. Horizontal
<br /> . _ distanoa=8184X.8869=518.09 ft,
<br /> S�a� Ap4�e Horizontal distance also=Slope distance minim slope
<br /> V distance times(1—cosine of vertical an�g►eL With the
<br /> same figures as in the preceding eaamp a.the follow-
<br /> Horizontal distance ing result is obtained.Cosine b°1M—.88b9,1—.9969=.004L
<br /> 819.4X.0041=1.51.519.4-1.51=518pa�!t
<br /> When the else is known,the horizontal distance is appl-12- telt':—the Slope dist
<br /> -
<br /> nce less the square of the rise divided by twice the slope distance. Thus:rise=14 ft,
<br /> dope distance-505.8 ft Horizontal distanoe=5018—14 X 14=5028-0.55•30&28 ft.
<br /> 1 5 X 592.8,.'
<br /> MADE IM U.S.A, J-
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