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<br />;� -77
<br />TRIGONOMETRIC FOR gULfE
<br />B B B
<br />c. a c a c a
<br />• b C A�b G' A C
<br />Right Triangle Oblique Triangles
<br />Solution of Right Triangles F,
<br />a b a b c rl�
<br />For Angle A. sin = c , cos = c , tan = b , cat = a , sec = b , cosec =
<br />a
<br />Given Required I
<br />a
<br />a, b �,'B ,c tan A = a = cot B, c = 1I"x"- i"= rc 1 -} Fri '
<br />b � a- .'V
<br />a, c
<br />A, a B,'&, ca
<br />B=90°—A, b = cccot A,d=
<br />sin A.
<br />A, b B, a., c B =90'—A, a = b tan A, c = b 1t��' I
<br />cos A. V \. t'.
<br />A,c B, a, b B=90°—A,a=csin A,5=ccosA,
<br />J
<br />Solution of Oblique Triangles -7�
<br />Given Required'I
<br />A, B,tc h, c, G'.. b=ryinn.4'C=1809-' tA+B),e,=an`A ` -
<br />a
<br />A, a, b B, c, C sin B = b sin A G' = 180"—(.4 -i B), c si
<br />a = sin
<br />a,
<br />b, .0 A, B, c A+B=180°=.C, tan :4(a—B)=(a—b) t$n ;
<br />a+b
<br />,a sin C
<br />>in A .
<br />a, b, c A, B, G' s = 2 ,sin 4:1=. b c '
<br />i
<br />sin'B=,/ a c
<br />a, b, c Area s= , area = %%a(s'—a) s— )(s—c) r
<br />h e sin A
<br />A, h, c Area jl t
<br />area = 2 D
<br />a" --'sin B sin C
<br />A, B, C, a Area area = 2 sin A
<br />REDUCTION TO HORIZONTAL Q -
<br />Horizontal distance=Shope distance multiplied by tlie5 i 7^
<br />cosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />tstanco Vert. angle -51 101. Frem Table, Page IX. cos 5° 1tY=
<br />ove a N 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />5� Angle Horizontal distance also=
<br />-
<br />Slope distance minus slope
<br />tied. distance times (t—cosina of vertical angle). With the
<br />same figures as in the preceding example, the follow-
<br />ing result is obtained. Cosine 50 10'=.9359. 1—.9959=.0041.
<br />319.4X0041=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 ft. Horizontal distance=3026— Ut X 14 =3026-0.32=302.28 ft.
<br />i " X 302.6
<br />k MADE IN U.S.A.
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