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l � TRIGONOMETRW FORMULA]-
<br />p,�t'l `1-�-. � �v � r, it -a •t�`]'a, 1.7j�,• Ca.: J � B 13
<br />i A. A C
<br />C
<br />Right Triane[e (- Oblique Triangles
<br />l �►ti" p ; y s Solution of Right Triangles
<br />a b a_ b c e
<br />le Far Angle d.: sin = - cos = s rau = , cot = - sec = -, cosee = -
<br />�'q ta' b d
<br />f �` '_ f t, ✓ � ` 1 �I. - 3 Given Required 2 a
<br />$ \ _ ^� a,b A,IJ,e tan A=b= cot B,c= a j b =a 1+aa
<br />V 1 `1;�:� . ' a, c d, Br b rind = = cos l3, L = i/ (o l a7 1 -- o Z
<br />� •�; ,✓ `- `� B, b, c B=90° -A, b = acotA,c= a
<br />Ein A.
<br />Z '
<br />, / a A, b B, a, c B = 90'-A, a = b`tan A, c
<br />cos A.
<br />A., c A a, b B= 90°-A a = c sin A, b= e cos d
<br />Solution of Oblique Triangles
<br />Given ' tlevuired 2'sin i3
<br />d, B,a b, c, C b- ,C=1S0°-(d+B),c-asinG'
<br />sin sin ?i
<br />bsin A
<br />._ . ,, \ a A, a, b 13, e, -C sin B = a , C = 180°--(A s n A
<br />L ,\ y
<br />ca, b, C A, B. c A+ 13=180°- C, tan ?: (A -.B)= (2-b) tan a
<br />+ a '
<br />a sin C
<br />�j ti sin.A
<br />• '• x'73 a+b+ ; !'$
<br />��Tl
<br />LY a, b, e A, B, C s = sin A = j 2 - be
<br />6.
<br />I\XL
<br />���
<br />�3 �
<br />\; e Area �- area = s(x-cr) ie -b) (s c
<br />A, b, c Area area = b e sin .4
<br />�`A -- 2
<br />VVYO
<br />d, B, G; a Area a' sin .8 sin (;
<br />area =
<br />ArL�iofi�� t' 2 sind ,
<br />% REDUCTION TO HORIZONTAL
<br />�� „ �r U Horizontal distance —Slope distance multiplied by The
<br />cosineofthevetticalangle.Thus:slopedistance=319.411.
<br />h I s \ a�sto�e N q°ort. angle=5° 10'. From Table, Page IX. cos 5° 10'=
<br />r ^ c 59. Horizontal distance=31J.4X.9950=318.03 ft.
<br />a V 51o'p Pnr�e a
<br />Horizontal distance also=Slope distance minus slope
<br />j A• ' f14 ' a distance times (1—cosine of vertical anwie)• With the
<br />figures as in the preceding example, the follow -
<br />Horizontal distance ing result is obtained. Cosine
<br />5° 10'=.9359. L—.9359=.0041.
<br />819-4X.0041=1.31. 319.4-1.31=318. ft.
<br />1.
<br />When the rise is known, the borizontal distance is approximately:—the slope dist- r'
<br />r } ante less the square of the rise divided by twice the slope distance. Thus: rise=loft., y
<br />4' +
<br />slope distance=302.6 ft. Horizontal distance=3026— 14 X I4 =302,6-0.32= 301.23 ft,
<br />2 X Ant -S
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<br />NAGE IN U.S.A.
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