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<br />47I Al, O 1-,,/ 6 Vrc
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<br />�. Z'
<br />0 el 9,
<br />30
<br />TRIGONOMETRIC--FORMULfE
<br />ll o c
<br />o -7 Z e
<br />a a c a
<br />A
<br />A
<br />C, �b C A b C
<br />Oblique Triangles J
<br />b
<br />_ Right Triangle
<br />Solution -of Right Triangles
<br />For Angle A. sin = a ,cos = b a ,cot = b ,sec = cosec =
<br />c c b b'
<br />Given
<br />a,b
<br />Required
<br />-A,B,c
<br />a a
<br />tanA=b=cotB,e= a2+b2=a 1 } 2
<br />L
<br />a
<br />Q, o
<br />A., B, b
<br />sin A = o =cos B, b = \/ (c 1 a) (c—a) = c � 1— a
<br />A, a
<br />B, b, c
<br />B=90°—A, b= a cotA, c= a
<br />sin A.
<br />A, b
<br />B, a, c
<br />B =900—A, a = b tan A, c = b
<br />�
<br />cos A.
<br />k A, c
<br />B, a, b I
<br />B = 900—A, a = c sin A, b = c cos A,
<br />Solution of Oblique. Triangles
<br />Given
<br />-A, B, a
<br />Requireda
<br />b, c, C
<br />sin B C
<br />b _
<br />' C = 1800—(A + B), c =
<br />_ sin A sin
<br />sin A
<br />A, a, b
<br />B, c, C
<br />b sin A
<br />sin B = , 0'= 180°—(A + B),c c = a sin C
<br />a sin A
<br />a, b, C
<br />A, B, c
<br />A+ B=180°— C, tan '2 (A—B)= (a—b) tan z (A+B)
<br />r �
<br />`
<br />>
<br />a sin C + a b
<br />sin A
<br />I. a b c
<br />>
<br />A, B, C
<br />s=a+b+c , I s—b)(s—c
<br />,sin aA=
<br />2 b, '
<br />sin ;B=—c) C.=180°—(A+B)
<br />ac
<br />a, b, c
<br />Area
<br />s.=a+2+c, area = N/8(8—a (s—b)(s—c
<br />i A, b, c
<br />Area
<br />b c sin A
<br />area =
<br />2
<br />i
<br />A, B, C, a
<br />Area
<br />a2 sin B sin C
<br />area =
<br />2 sin A
<br />.. REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />arpe
<br />ass\
<br />Vert. angle =5° 101. From Table, Page IX. cos 50 lol=
<br />g\ope
<br />9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />Horizontal distance also=Slone distance minus slope
<br />-'je
<br />a distance times (1—cosine of vertical angle). With the
<br />same figures as in the preceding example, the follow -
<br />Horizontal distance
<br />ing result is obtained. Cosine 5° 10,=.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.
<br />Horizontal distance=302.6— 14 X 14 =302.6-0.32=302.28 ft.
<br />2 X 302.6
<br />MADE IN U.S.A.
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