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<br />210 -
<br />TRIGONOMETRIC
<br />3a
<br />TRIGONOMETRIC FORMULAE
<br />R
<br />6a
<br />. c w �
<br />vu a a a
<br />� b' C At C `4 L 1 �
<br />Right Triangle Oblique Triangles ,
<br />Solution of Right Triangles
<br />For Angle A. sin= ° , coo= b , tan= a , cot = b , sec = a , cosec = e
<br />c o b a b a
<br />(liven Required a 2
<br />Ca,b A,B;o tan A=b=cotB,c= az+ 2=a V,+a2
<br />2
<br />a, a A, B, b sin A = = cos B, b = �/ (c-� ¢) (c —a = e 1— o
<br />A, a B, b, c B = 900—A, b = a cot A, c =
<br />sin
<br />A.
<br />' b
<br />A, b B, a, c B = 90°—A, a = b tan A, c= � cos A.,
<br />{ A, c B, a, b I B = 90°—A, a = e sin A, b = c cos A,
<br />Solution of Oblique Triangles
<br />i (liven Required a ein B¢sin C
<br />A, B, a b, c, C b = in A , C = 180°—(A + B), c = sin A
<br />l,- b sin A a sin C
<br />F
<br />A, a, b B, c, Csin B= a ,C = 180°—(A { B), c = sin A
<br />a, b, C A, B; o A+B=180°—C, tan lj(A—B)=(a—b) can' (A+B),
<br />a + b
<br />a sin C
<br />c=
<br />sin A
<br />a, b, c A, B, C s=a+2+c,einA=Y(s ba
<br />sin JB=1l(s—a) s� ,C=180°—(A+B)
<br />Y a G
<br />—a+b-{ a
<br />a, b, c Area s— 2 ,area = V15(s—a s— s—c
<br />A, b, c Area area = b a sin A
<br />2
<br />a= sin B sin C
<br />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 ft.
<br />tsope Vert. angle=51 101. From Table, Page IX. cos 50 10'=
<br />oPe ass y 9959. Horizontal distance=319.4X.9959=31&09 ft.
<br />g1 XaXe x 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 60101=.9959.1—.8959=.0041.
<br />319.4X.0041=1.31.319.4-1.31=31&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 M.
<br />slope distance=3028 ft. Horizontal distance=3020— 14 X 14 =302.8-0 32=30228 ft.
<br />2X=8
<br />MACE IN V. S. A.
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