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TRIGONOMETRIC FORMULAE'
<br />7 } E B B
<br />�2I_Z 2b t v
<br />TP
<br />A� b
<br />9' Right Triangle C Oblique Triangles
<br />• Solution of Right Triangles
<br />•3.43, , 103, 43 t• a b a b c a
<br />For Angle A, sin = c ,cos = c ,tan = b ,cot = a ,sec = b , cosec =
<br />a
<br />Given Required a
<br />A, B ,c tan A = a b = cot B, e = 1V as + z = a 1 -i- az
<br />L'v l� a;c A,B,b a—
<br />I sin A = = cos B, b = �/ (c a) (c—a) = c 1-
<br />- } 02
<br />A, a B, b, e B=90°—A, b= a cotA, c=. a
<br />1 �l���11"�''' sin A.
<br />% — f
<br />A,b
<br />B, a, c B=90°—A,a=btan.A,c= b
<br />•�
<br />cos A.
<br />_ A,c B,a, b B=90°—A,a=csin A,b=ecosA,
<br />�' t1 Solution of Oblique. Triangles
<br />Given Re4hired
<br />r a.
<br />A, I3, a b, c C b.= asin B C='180°—(A B}, c= asin C
<br />sin A sin d
<br />5- z tt b sin A a sin' C
<br />A, a, b B; q C sin B= a A.
<br />=.180'—(A + B), o = sin A
<br />Z7 0 a, b, C A, B,-c. 4+B=180°— C, tan'(A:--B)— (a�b) tan (A �B) c _ a sin C a } b
<br />f
<br />sin A
<br />a' b' e A'B,C s=a+ G,sin1..9.=`!.e—be
<br />5i»!-B ae c=iso°—(4+B)
<br />zG�= a+b1c
<br />Q ; .. : t•, '� a, b, c Areas = 2 ,area = V's (.ti—a) (s— ) (s—c
<br />bcsin A �l �•
<br />A, b, c Area area _- L
<br />Area
<br />B, a2 sin B sin C
<br />G; aarea = 2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal'distance =Slope distance multiplied by the
<br />jia��� cosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />tq at�pe' Vert. angle =5° 10'. From Table, Page IX. cos BOW=
<br />�. tk ass` m 8958: Horizontal distance=3]9.4X.9859=315.09 ft. +s
<br />o4e "1e a Horizontal distance also=Slope distance minus slope
<br />lr 1 d/ t. P distance times (1—cosine of vertical angle). With the
<br />`Ie same figures as in the preceding example, the follow-
<br />' Horizontal distance ing result is obtained. Cosine 5°,
<br />0'=.9959.1—.8959=.0041.
<br />319.4X.0041=1.31. 313.4-1.31=310.09 ft.
<br />When the 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=14 ft.,
<br />11 r slope distance-302.617t. Horizontal distance=302 0-2 X 30I& =302.0-0.32=302.28 ft.
<br />MADE 1N U. a, A.
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