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TRIGONOMETRIC FORMULAE
<br />q- a a c a c a
<br />� J g A A G, u
<br />C b ;
<br />t , Right Triangle Oblique Triangles y
<br />Solution of Right Triangles
<br />l.. a b a- b c e k
<br />�. _. .. 'For Angle A. sin = a , coe = a , fan = b ,cot = a , sec cosec 7
<br />i � a
<br />1� © 1. � Uiven Required �y' z r
<br />a, b A, B ,c tan.A = b =,cot B, o = a$ -1 z = a 1 f —
<br />a2
<br />as a - A, B, b
<br />sin A = a = co B, 6 = (a-♦ (e—a) = c p 2
<br />;.A, a B, b, c B = 90°—A, b = a cot A, 4 = ¢
<br />si bA. h
<br />A, b B, a, e B = 90'—A, a = b tan A, c = coe A.
<br />/ �--- A, c B, a, b B =90` --A, a = e sin A, b = o cos A,
<br />£ Solution of Oblique Triangles
<br />Given Required asin B` ¢in C
<br />'A, B, a
<br />sin A C — 180"—(A + B) e
<br />a =
<br />sin A
<br />b ein A a sin C
<br />A, d, b B, c, C sin A= a . C = 180'—(A -l- B) sin A
<br />a
<br />_ i a, b, C A, B, a A+BA180°— C tan (A—B)= (a—b) can (A+B)
<br />f / ' afb
<br />o
<br />p, �t
<br />sin.A
<br />' a, b, o A, B, C S=a+2+e,eia be
<br />sin JB= ( ae C=1800—(A+B)
<br />/
<br />bt
<br />4� o, , c Area ,area = a(a—a a— (8�
<br />2.
<br />A, b, c Area
<br />b. a sin A
<br />- area =
<br />C, a Area area = ag sin B sin O
<br />2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance—SIope distance multiplied by the
<br />cosifie of the vertical angle- Thus: slope distance=319.4ft.
<br />% 5�oc Vert angle -50 10'. From Table, Page IX. cos 5° 10'=
<br />_ Y ! �m 9 A Horizontal distance =318.4X.9959=318.09 fL
<br />y.10 .1
<br />Horizontal distance also= Slope distance minus slopeta
<br />distance times (1—cosine of vertical angle). With the
<br />y same fi¢ures as in the preceding example, the follow- `!
<br />Horizontal distance tng result is obtained. Cosine 5° 10,=.9958.1--9959=.0041.
<br />319.4X.0041=1.31.919.4-1.51=31&09ft 1
<br />When theAse is known. the horizontal distance is approximately:—the slope dist-
<br />trice less the square of the rise divided by twice the slope distance. Thus: rise=l4 rL,
<br />s 14X14=
<br />� elope distance=9028 !t. Horizontal d[etsace=9028— 3026-0.32=30228 M
<br />2x=8
<br />' � - MAOE IX U. B. A.
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