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"Y 89 Go
<br />5-6 33
<br />33°7'
<br />y3. (%
<br />A; TRIGONOMETRIC F.RMULfE
<br />� B G7� S B
<br />(� I c ac a c a
<br />I C
<br />A f' b Cf CA
<br />Right Triangle Oblique Triangles
<br />Solution of Right Triangles
<br />!i a b a b c c
<br />Fo;iAngle A. sin = c ,cos= c , tan= b', cot ='a , see = —b, cosec =
<br />a
<br />'Given Required
<br />z 2 � }a, b A, B ,c tan d = b = "dot B; c = ¢2 + = a 1 -I- az
<br />!a; c A, B, bsin A = c = cos B, b = \/ (c+a) (c—a) = c l — a
<br />a
<br />Aqq a B, b,'e 'B=90°—A, b = a cotA, c= sin A.
<br />A, b B, a, c B = 90°=A, a =_ b tan A, c=
<br />cos A.
<br />A, c B, a, b i B = 90°—A, a = c sin A, b = c cos A,
<br />Solution of Oblique Triangles
<br />Given Required
<br />A, B,a b, c, C b=asinB C=180°—(A+B),e=¢sinC
<br />sin A sin A
<br />A, a, b B, c, C sin B = b sin A , C = 180°—(A f B) a sin C
<br />a , c = sin A
<br />a; b, C A, B, c . A+B=180°—C, tan z (A—B)=(a—b) tan
<br />+ (A+B),
<br />( a sin C
<br />� c =
<br />sin A
<br />¢--b -I o �(s— b)(s—c
<br />2
<br />a, b, c A, B, C s= .,sin ',A= b c '
<br />sinB= \I a c , C=180°—(A+B)
<br />a+b+
<br />a, b, c Area 8— 2 , area = s(s—a
<br />4A, b, c Areab c sin A
<br />area = 2'
<br />a2 sin B sin C
<br />A, B, C, ¢ Area area = 2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance=Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slope distance=319.4ft.
<br />t�nce Vert. angle =5° 101. From Table, Page IX. cos 50 101=
<br />aye y 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />e
<br />shop Ar��e Horizontal distance also=Slone distance minus slope
<br />f Ve a distance times (1—cosine7of vertical angle). With the
<br />same figures as in the preceding example, the follow -
<br />Horizontal distance ing result is obtained. Cosine 5° 101=.9959.1—.9959=.0041.
<br />319.4X.0041=1.31. 319.4-1.31=318.09 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 />slope distance=302.6 ft. Horizontal distance=302.6— 14 X 14 _302.8-0.32=302.28 ft.
<br />2 X 302.6
<br />quos is U. s. A.
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