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<br />+j �, %� i�o� TRIGONOMETRIC FORMULfE
<br />a. c c
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<br />em
<br />f -Right Triangle Oblique Triangles
<br />Solution of Right Triangles,
<br />E7� b2 _ a _ b _ ab- c
<br />" For Angle A. sin - cos - .- , tan - , cot = -,see see - -, cosec =
<br />c' X33 b. a b a.
<br />Given -Required'
<br />r^�u "Z a,b A,B,c tan A=b=cotB,o= az+ s=a 1+aa
<br />1.,..q. _ --- - - - T - a. A B;.,b einA = =cos B, b=�/ 3+a (c --a) c 1-ars
<br />e = s
<br />`�` a o
<br />°,4 f�, A,a B, b, c B=90°-A,b=acotA,0
<br />/• Oa% doQb �` Bina
<br />A, b B, a, c B= 90°-A, a= b tan A c=
<br />/': Gi.J 6 ' • p0 b y A cos .i.
<br />- / •3 A, c B, a, b 'B = 90°-A, a = c gin A, b = e. cos A,
<br />n
<br />3�
<br />415- M�; r'• 1, t d ¢ Solution of Oblique Triangles
<br />3 Given Required
<br />aeiaB , aein C
<br />A, B,a a,.q C b- sinA'C=180 (A f B},a= sinA
<br />e .�q b sin A a sin C
<br />f 3 33 d l O v 3 0� Ay a, b B, c, C sin B= a ,C = 180°-(A B), c= sin A
<br />/ (a -b) tan a (A+B)
<br />Sco 7 q /, ri Pao S % G _� �✓ -t � ati b, C A. B. a A+B-180°- C, tan } (A -B)=
<br />2,.3 S
<br />rlsD �9�`�' �! asinC
<br />0 ° �b
<br />/, ! o = sin A
<br />a+
<br />a, b, o A, B, C a_2+
<br />c,ein.''A= N(a be
<br />sin +}B-m� ) C-180°-(A+B
<br />�
<br />a.a+b+c
<br />' = YY
<br />b,'c Area
<br />S _ -r i 2
<br />y �a`i 7• I �ObL3 b.asin A
<br />'� _ 0• �y 0 3 j
<br />30 i A, b, c Area area = Z
<br />2 9 ,� S 0 -3
<br />a' sin B sin C
<br />p
<br />Q' X33-67` 3���'g fi A, B,C,a Area area = 2sin A
<br />c1`� �� l• ���+ .5 J REDUCTION TO HORIZONTAL
<br />% I Horizontal distance= Slope distance multiplied by the
<br />ee cosine of the vertical angle. Thus: slope distance =319.4ft
<br />�S�ao q Vert.
<br />9959. Holrzontal distance 19.4X.9959 3 &09 ftJY_ cos 5° id=
<br />NH .' S�° Ap¢1C a Horizontal distance also= Slope distance minus slope
<br />qe distance times (1 -cosine of vertical angle). With the
<br />%
<br />Horizontal distance same figures as in the preceding example, the follow-
<br />ing result is obtained. Cosine 50 10Y=.9959.1-.9959=.0041.
<br />319.4X.0041=1.31. 319.4-1.31=318.09 ft. .
<br />When lhe•rise is known, the horizontal distance is approximately: -the slope dist-
<br />ance less the square of the rise divided by twice the slope distance. Thus: rise=l4 ft.,
<br />slope distance=3020 ft Horizontal distance=3028-2 X 14 =3028-0.32=30228 M
<br />t,�V 1 y� _.` , i • 1 Ifo MADE IN V. 8. A.
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