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ev
<br />33
<br />0
<br />-- /07 - Z T-
<br />7 s 8 S-11
<br />--4+7
<br />j
<br />r*
<br />X 4
<br />TRIGONOMETRIC FORMULR
<br />B B
<br />C
<br />a a
<br />Ab 0 A A C
<br />Right Triangle b 0,
<br />Oblique Triangles
<br />Solution of Right Triangles
<br />b 0
<br />For Angle A. sin a cos -- a b tan= —b , cot = a , sec cosec = a
<br />Given Required _F2
<br />di b A, B,c tan Acot B, c a
<br />b +77a2
<br />A, B, b sinA=— = cos B,b=\/(o+aT(o—a)=e 1
<br />all
<br />A, a B, b, a B=90°—A, b = a cotA, t,— a
<br />sin A,,
<br />A, b B, a, c B = 900—A, a,= b tan A o
<br />cos A
<br />A, B, -a, b B = 90'—A, a = c sin A, b =-0 cos A,
<br />Solution of Oblique Triangles
<br />Given Required b�= asin B. 0 = a,in C
<br />��A, B,a b, e, C Sin A C = 180--(A + B), sin A
<br />A, a, b B, 0, C sing= b sin A G = 180'—(A + B), c = a sin C
<br />a sin A
<br />b, C A, J1, c A+B=18V— C, tan 1 (A—B)= (a—b) tan I' (A+B
<br />a sin C +
<br />sin A
<br />b (8—
<br />i a, b, a A, B, C 8=a+2+o 'gin IIA= N i )(8—c)
<br />sin'B(s—a)(s—c),C=180* —(A+B)
<br />=
<br />ac
<br />b
<br />b, Area a+2+ , area = VrS (8 aTTs--V) (7---e)
<br />b 0 sit) A
<br />A, b, o Area area = 2
<br />all sin B sin C
<br />!A, A 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 husi slope distance =319.4ft.
<br />From
<br />ze Vert. angle = 5' 101. Table, Page ix. cos 50 10—
<br />.9959. Horizontal distance=319.4X.9959' 318.09 ft.
<br />51op0
<br />o,%e -2 Horizontal distance also�Slope distance minus slope
<br />distance times (1—cosine of vertical angle). With the
<br />e figures as in the preceding example, the follow -
<br />Horizontal distance ing result is obtained. Cosine 50 101=.9959. 1—.9959=.0041.
<br />319.4X.0041=1.31.319.4-1.31=318.09 ft.
<br />When the rise Is known, the -�orizontal distance is approximately:—the slope dist-
<br />a,nce less the square of the rise divided by twice the slope distance. Thus: rise=14 ft.,
<br />slope distanee=302.6 ft. Horizontal distance=302.6— 14 X 14 =302.6-0.32-302-28 M
<br />2 X 302.6
<br />MADE IN U.S.A.
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