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<br />TRIGONOMETRIC FORMULlE 1, / Z
<br />B B B
<br />c
<br />C a a c a / ,
<br />A b C A�b O'. /b, C u
<br />Right Triangle Oblique Triangles
<br />Solution of Right Triangles
<br />For Angle A. sin = a , cos= o , tan= b , cot = a , sec = b, cosec = a
<br />Given Required a a
<br />a,b A,B,c tan A=b=cotB,c= aa+ a=a 41+ a$
<br />_
<br />a, o A, B, b sin A = o = cos B, b = V (c+a) (c --a) = c 1—EL
<br />L
<br />A, a B, b, c B=90°—A, b= a cotA, c= a
<br />sin A.
<br />' b
<br />A b B, a, e B = 90°—A, a = b tan A, c = cos A. •
<br />A, a 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 = a sin B C = 180°—(A + B), c = a sin C
<br />sin A sin A
<br />A, a, b B, e, C sin B= b sin A, = a sin C
<br />C
<br />a 180 —(A } B), c = sin A
<br />a, b, C A, B, c A+B=180°— C, tan (A—B)— a=b) tan a(A+B)�
<br />a +.b
<br />c=
<br />a sin C
<br />sin A'
<br />f a+b+cI(s—b)(s—c
<br />a, b, a A, B, C s= 2 ,sin;A= bo '
<br />ein,B= J ac C=180° (A+B) .
<br />i -
<br />;� a+b+c
<br />a, b, e, Area s= 2 ,area
<br />1 A, b, c Areaarea = b e sin A
<br />2
<br />�I
<br />a a sin B sin C
<br />i A, B, C, a 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 =319.4 fL
<br />�Qope Vert. angle= 50 101. From Table, Page IX. cos 50 10-
<br />Ce ass y 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />$"o AngNe a Horizontal distance also=Slope distance minus slope
<br />Qe �. distance times (1—cosine of vertical angle). With the
<br />same figures as in the preceding example, the follow -
<br />Horizontal distance 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. Horizontal distance=3026— 14 X 14 =3M6-0.32=302.28 M
<br />2 X 302.6
<br />MADE IN V. S. k
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