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_ TRIGONOMETRIC FORMUL&
<br /> aa
<br /> c a c
<br /> r � -
<br /> f.. �:.
<br /> AA C
<br /> b C �b C ,
<br /> -Right Triangle Oblique Triangles
<br /> Solution of Right Triangles
<br /> /G a For Angle A. sin = ,cos= ,tan= b,cot = a,eec= b, cosec= a
<br /> Given Required
<br /> a, b. A, B,c tan A=b= cot B,c = a
<br /> 2 •
<br /> 2 } z =a 1 } $
<br /> O .r� a
<br /> a A, B, b sin A=a
<br /> Q=cos B,b= --
<br /> (ca (c-a =c J 1-
<br /> r '
<br /> ' o
<br /> A,a B, b, c B=90°—A,b =acotA,a= a
<br /> A, b B, a, c B=90°—A,a = b tan A,c=
<br /> cos A. -
<br /> Zl " " f A, c B, a, b B=90°—A,a=c sin A,b=c cos A,
<br /> r Solution of Oblique Triangles
<br /> J � Given Required a sin B
<br /> A, B' a b' c' C b sin A ' C= 180°—(A+B), a= sin A
<br /> b sin A a sin C
<br /> I a A, a, b B, e, C sin B= ,C= 180° +—(A B),o=
<br /> a sin A
<br /> 3. 3 d ?r" a, b, C A,B, c A}B=180°—C,tan a(A—B)= a—b a°� b �.
<br /> a sin C
<br /> c =
<br /> sin A y 7
<br /> a in A=
<br /> +b+
<br /> 4 csVis
<br /> s L b, c A, B, C 8= 2 bo z
<br /> sin;B=�(a-axa-c ,C=180°-(A+B)
<br /> / ac
<br /> _ ! a+b+c
<br /> g a, b, a Areas= 2 , area = s(s-a a-- (a-c
<br /> - sg
<br /> A, b, c Area area = b e i A
<br /> 3 -7 a2 sin B sin C
<br /> j r A,B,C,a Area area = 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 fL
<br /> j' ytit9� Vert. angle=50 10'. From Table,Page IX cos 60 10�=
<br /> / o4e a 9966. Horizontal distance=319.4X.9959=31&09 ft.
<br /> ` S� Apq�e Horizontal distance also=Slope distance minus slope
<br /> Qe distance times (1-cosine of vertical angle). With the
<br /> same figures as in the preceding example,the follow.
<br /> S t' 4� _ Horizoatal distance ins result is obtained-Cosine 60 1d=.9969.1-.990=.oki.
<br /> { 319.4X.69{1=L31.319.4-1.31=31&o91L
<br /> A' When the rise is known.the Lps�ta► :
<br /> distance is appeimately:-the slope dist-
<br /> f —e less the square of the rift di -"by{tribe the slope distance. Thus:rise=14 fL,
<br /> slope distance=301,6 fL l3ork00361 6-14 X 14-0Z6-0.32=302 ft
<br /> �`. 2 X 302.6
<br /> s ,
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