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9 U rZ 2 � l TRIGONOMETRIC FORMUL&
<br /> J�• P
<br /> I
<br /> 1/9;i3 - B B B
<br /> a c a c
<br /> A bA
<br /> C b C
<br /> Right Triangle Oblique Triangles-----�
<br /> Solution of Right Triangles
<br /> yQ �.� For Angle A. sin =a b a b G
<br /> G ,cos= ,tan= b ,cot = .a.sec= b, cosec= o
<br /> Given Required a a
<br /> a, b A, B,c tan A= b= cotB,o= a + z = a _
<br /> 1 as
<br /> 2'8 a, c A, B, bsin A=a=cos B,b=*,/ c+a a—a =G 1—o
<br /> 41 -2
<br /> A,a B, b, c B=90°—A,b =acotA,G= a
<br /> 3,40 Z sin A.
<br /> A, b B,a, G B=90°—A,a = b tan A,c= b
<br /> cos A.
<br /> " A, c B, a, b B=90°—A,a =c sin A,b= c cos A,
<br /> s t' .2 �' C Solution of Oblique Triangles
<br /> Given Required
<br /> '/, 79 •. r z f A, B,a b, G, C b= a sin B C= 180°—(A+B), c=a sin C
<br /> sin A ' sin A
<br /> A,C= 180 (A+B),o=
<br /> o;, b B,q p' sin B= o— a sin C
<br /> a sin A
<br /> Rz
<br /> A, B, c A+B=1800—C,tan j(A—B)=(a—b)tan A+B)IV
<br /> � - a sin C a-F b
<br /> sin
<br /> ` o.; A, B, C 8=a±b ,ein A— l8_ be—e
<br /> 2
<br /> ad C=180°—(A.i-B)
<br /> a, b, o, Area 8=a+— , area = 8(8—a 8— (8—e
<br /> `j 2.
<br /> 2 y A, b, c Area b e sin A
<br /> area =
<br /> Z7 fy •��'V l� az sin B sin C
<br /> A,B,C,a Area area =
<br /> � Fain A
<br /> q � REDUCTION TO HORIZONTAL
<br /> n / Horizontal distance=Slope distance multiplied by the
<br /> cosine of the vertical angle.Thus:slope distance=819.48.
<br /> - a d Vert. angle=6o 101. From Table,P 5o
<br /> ,W=9869. Horizontal d1stance=819.4X.99 818.09 ft,b id=
<br /> \ � Z 9
<br /> Horizontal ti distance also=Slope distance minni slope
<br /> U( ye distance times(1—cosine of vertical angle): With .
<br /> same figures as in the preceding example,the follow-
<br /> ` ry ' Horizontal dlagtaop ing result is obtained.Cosine 60 10,=.9969,1—•9969=.QM.
<br /> 819.4X0041=1.81.819.4-1.81=81&09 ft.
<br /> When the rise is known,the horizontal distanceefln is approximate) -the elope dist-
<br /> ance leas the square of the d"dl �1pp�
<br /> slopedistance=80208 Hortzoa delis 1�XH distanee, us.rlse=14ft.,
<br /> 30
<br /> 2 X 902.8 2.8—&32=30&2B fL
<br /> MADE IN U.4.A.
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