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—^J1J TRIGONOMETRIC FORMULAE
<br />• - � a a
<br />G, 4A b C ti b C �--
<br />�,' Right Triangle Oblique Triangles !
<br />•�`-rl , ' -y Solution of Right Triangles
<br />a b a b c c
<br />For Angle A. sin = c cos= o , tan= b , cot = a , sec = b, cosec =
<br />a
<br />L._:_'_7.•, I / Given Required
<br />1 1 I_• '� �{ ' '� ��L�b .L� o �U l �h d 0 ci 2, b _4, B ;c tan _A = b = cot B, c ti = a IT 2 ,
<br />1 ` a
<br />-1, B, b sin A = c =cos B, b,='.,1 (c a) (c—a) = c 1 - a2
<br />V �� v. Volo J C,o I c{ l� j0 A,a B, b, c 8=90'—l,b=acot l,c= a
<br />cn C, U'v i sin 4.
<br />4, b -B,-a, c B= 90'—A, a= b tan 4, c= b
<br />cos A.
<br />can evr ���1a� A,c B,a,.b B=90°—A,a•=csin A,b=ccos 4,
<br />' = .' • (jai - Solution of Oblique Triangles °
<br />Given Required a sin Br _
<br />Ccv�tb, A, B, (& b, c, C b= ,C=180'—(-4-1-B),c=as
<br />s. n 4
<br />y :
<br />� sin A-
<br />_ d , b sin 4 fi a•si
<br />A, a., b B, G c, ' sin B = a C = 180 —(A B)n C, c
<br />_ sin A
<br />Ln a, b, C A, B, c -4-rB=180'— G', tan , (_9—B)- (alb) ¢ +
<br />a sin G - r••
<br />n Qgoo
<br />' sin 4 A,
<br />a, b, c A, B, G' 4_cai b+c
<br />sin 4A=
<br />2 ,
<br />VVVII b e
<br />' \ sin B=i,G 0=180°—(A+B)
<br />ko b, c Area s= +u+ area = %/,q (s—a) (3
<br />G 1.8 0 �b _ 1'• �A, b, e Area b e sin A
<br />area = 2 � ,
<br />a2 sin B sin C.
<br />A, B, .C, a Area area = 2 sin A
<br />C *moo •1� 1 5' `� 7 J� ! Al" c,. REDUCTION TO HORIZONTAL
<br />!� c n:�J �?•- �� j ( - 1 ` Horizontal distance=Slope distance multiplied by the
<br />° - cosine of the vertical angle. Thus:.siopedistance
<br />=3l0.4ft.
<br />Vert. angle =5° 10'. From Table. Page IX. cos 60 vy=
<br />y AA Horizontal distance=319.4X.9959=318.09 ft. IiorizontaI'd istance also=Slope distance minus slope
<br />- t• 1' distance times (1—cosine of vertical angle). With the
<br />(' �° same figures as in the preceding example, the follow-
<br />010 Horizontal distance ing result is obtained- Cosine 5'=.9959. 1—.9959=.041.
<br />319.4X.0041=1.31.319.4-1.31,=318.0j fl.
<br />/t-+
<br />' 1When the, rise is known, the horizontal distance is approximately:—the slope dist-
<br />2 ance less the square of the rise divided by twice the slope distance. Thus: rise=14 ft.,
<br />ov
<br />slope distance=302.6 ft. Horizontal distance=302.6— 14 X 14 =302.6-0.32=302.28 ft
<br />`.b ,� - 2X3002.6
<br />MADE IY U.B.A.
<br />--A
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