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PI
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<br />TRIGONQMETRIC FORMULAE
<br />15" 75'- ;"� a c a ° a '
<br />A a C..{
<br />i a• Right Triangle Oblique Triangles
<br />�. ,
<br />Solution of Right Triangles
<br />b
<br />• ..�. o�L?�� � • , a b -
<br />For Angle A. eiu = cos= .ten= b ,cot = a ,sec = b, cosec
<br />C C a �5
<br />Given Required
<br />y..-�
<br />72-
<br />Ix,b A,B,c tan A.==cotB,c=+mE
<br />dt,G A,B,b sink=e=cosB,b—l%(GI+z)(c—a)_eI—A2i
<br />-s
<br />g, a B, b, c B=30°—Ar b = a cntd, c= a ul
<br />sin A.
<br />A, b B, a, a B=90°—A, a = b tan A, c =
<br />cos A.
<br />A, a B, a, 'b B=90°—A, a = c sin A, b= a cos A,
<br />I(, Solution of Oblique Trianglesti
<br />S Given Required a sin B a sin G S
<br />A, B, a b. c, G b = sin A. ' C = 180°—(A. + B), c = sin A
<br />b sin Aa sin C
<br />A, a, b B, c, C sin B — ,�' 180°—(A + B)
<br />a sin A
<br />a, b, C A, B, c A+B=180'— C,.tan (A—B)— (a—b) tan (A 1 B)
<br />- - a + b R
<br />a sin C i }fir
<br />sin A.
<br />- i r
<br />a+b-)-a
<br />'j kt a, b, c A., B, ('i 81=2,sin qA= be
<br />sing— G-180°—(A+B) r.
<br />— ac _
<br />a, b, c Area s=a+b+c, area
<br />2 i
<br />0 A, b, c Area b c sip .A
<br />area = Z 1
<br />u
<br />_ A, B, C, a Area area = a= sin B sin C
<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 />�' aista�ce 9959. Horizontal distancle=51 101. e 919.4TableX. 958- 3 8.091t IX, cos 50 ld
<br />51a'Is Horizontal distance also= Slope distance minus slope
<br />i qe distance times (1—cosine of vertical angle}. With the
<br />4
<br />same figures as in the preceding example, the -follow-
<br />Horizontal distance ing result is obtained. Cosine 5° 10' .9859.1—.9959=.(1041.
<br />319.4X.0041=1.31.319.4-1.31=319.09 ft.
<br />When the rise is known. the horizontal distance is approxiinately:—the slope dist- y
<br />. _ ante less the square of the rise divided by twice the slope distance. Thus: rise=l9 ft, r r -- - y
<br />slope distance=902.8#t. Horizontal distance=3026— 14 X 14 =302 6-0.32=302E&.ft 9t
<br />/ - 2X3028
<br />r - S.-1, , - -y MADE IN U. A, I �f
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