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TRIGONOMETRIC FORMULAE
<br />f
<br />B B
<br />c.
<br />a c a ° a
<br />A A A b C
<br />Right Triangle, -C Oblique Triangles
<br />Solution of Right Triangles
<br />For ,Angle A. sin, = a , cos = b , tan= a , cot = b , sec = , cosec = a
<br />c c b a b a
<br />Given' Required
<br />a, b Al B ,a tan A = b = cot B, c = az+ z a 1 + az
<br />L:�(+ o$
<br />• a, c � B, b sin A = =cos B, b = (o+a) c—a - c
<br />A; a B, b, c B = 900—A, b = a cot A,, c= a
<br />sin A.
<br />A, b B, a, c B = 90°—A, a = b tan A, c — b
<br />cos A.
<br />A, c B, a, b 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), 0—
<br />s Ain C
<br />sin A ' sin A
<br />b'sin A a sin C
<br />A, a, b B, c, C sin B= a ,C = 180°—(A + B), c = sin A
<br />i a, b, C d, B, c A+B=180°-0, tan J(A—B)= (a—b) tan 1'(A+B)a +
<br />cb ,
<br />=
<br />a sin C.
<br />sin A
<br />a+b+c
<br />a, b, c A, B, C s= 2 ,sin3A= b e
<br />sin;B=� s—air c —
<br />,C=180°(A+B)
<br />a+b}c
<br />a, b, c Areas = 2 ,area = s(s—a s— ) (s—c
<br />A, b, c , Area area = b c sin A
<br />2
<br />A, B, C, a Area area = az sin B sin C
<br />2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance = Slope distance multiplied by the
<br />1 cosine of the vertical angle. Thus: slope distance =319.4ft.
<br />e�,",,,,,ce,
<br />Vert. angle=5° 101. From Table, Page IX. cos 5° 101=
<br />'9959. Horizontal distance=319.4X.9959=318.09 fL
<br />slopa Horizontal distance also= Slope distance minus slope
<br />Ve 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 51 10l=.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 YL Horizontal distance=302.6— 14 X 14 =302.6-0.32=302.28 ft.
<br />2 X 302.6
<br />s -
<br />MADF
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