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<br />IL
<br />ILI
<br />07
<br />Y
<br />TRIGONOMETRIC FORMUL&
<br />B B
<br />a aa
<br />C .
<br />A. A
<br />b C f b - a . . b
<br />Right Triangle Oblique Triangles
<br />Solution of Right Triangles
<br />a a
<br />For Angle -A. sin a cos b tan .= T i cot b —, sec cosec cos
<br />a
<br />Given Required 72-
<br />a, b
<br />A, B,o tan A cotB, o w+ =a
<br />a, e, A, A b sin Ac6s B, b \/TF+a) —(c—a) c
<br />7 02
<br />A,.a B, bt o B=90°—A, b a cotA,.o= a
<br />gin A.
<br />A, b B, a, o B = 900—Aj a b tan A,
<br />cos A.
<br />'A, c B, a, b I B=900—A, a = o sin A, b = o cos A,
<br />-Solution of Oblique Triangles
<br />Given 44 Required, a sin B a sin C
<br />b --:- — —(A- + B), 0 = -
<br />A,. B, a b, c, C sin A , C 180*. sin A
<br />A, a,. b B, c, C sin B.= b sia_A a = 180*—(A ( B), a sin C
<br />a sin A
<br />'(A+B)
<br />a, b, C A, B, A+B=180*-�- C, tan J,L(A—B)= a—b) tan 4 1 1 .
<br />a sin C +
<br />sin A
<br />a, b, o- A, -B, C =a+b+ , -,in_2'A=
<br />2 b.o
<br />sinl2B=� do C=180*-,-(A+B)
<br />a+b+c
<br />!%, b; *c Area s = 2 .area =,N/8 s—aTT (s -c).
<br />A, b, o Area b o -sin A
<br />area 2
<br />A
<br />a2 sin Ain C
<br />--- B, a Area 2 sin A
<br />C,
<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 />'Ce Vert. angle= 59 lV. From Table, Page IX. cos 51 IDI=
<br />'Ve .9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />'�"o oe Horizontal distance also= Slope distance minus slope
<br />-4e distance times (1—cosine of vertical angle). With the
<br />same ores as in the preceding example, the follow -
<br />Horizontal distance ing result is obtained. Cosine 50 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 distanee=302.6 ft. .Horizontal distance=302.6— 14'X 14 =302.6-0.32=30228 ft.
<br />2 X 302.6
<br />MADE LK U. G.A.
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