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<br />fv '`' f 1- TRIGONOMETRIC. FORMULtE
<br />A A
<br />_ C b G
<br />v�" ? Bight Trianglblique Tr
<br />Triangle Oiangles
<br />•� , �-- Solution of Right Triangles
<br />Far Angle A. sin = a —,coo= e —plan= b ,cot = , a , scc = b , cosec = ¢
<br />.►� .
<br />1 en .Required a z
<br />b 4,B,o tanA=b= cot B,c= aQ z=a 1 a
<br />1—
<br />A, 13, b sin A==cosB.b=�(c+�)(a—a) az
<br />a J. ;
<br />f _ c oa.
<br />B, b, c B=90 —A, b = a cotA, c=
<br />i} sin A.
<br />JjfJ B,, a, o B=90°—Aga = btan A,c=
<br />E cos A.
<br />A, c B; a, b B = 90°—A, a c sin A, b = e cos A,
<br />ti 2 ! s Solution of Oblique. Triangles
<br />Glfen Required a sin B a sin C
<br />E A, B)
<br />B, a b; c,.0 b C 180°—(A era A ' - +, c = sin A
<br />;-
<br />beraA asin C
<br />c, sing= a ,C = 1$0°—(A B), c = s00
<br />in A
<br />F.t(a—b)tan xr. }(A B b, C A, B, a A+B=180°-0, tan l(A—B)"— i )
<br />1_0Z
<br />r 4 p14 ; 1` a✓ a sin C
<br />a+b
<br />^ ern A
<br />A, B, C s — 2 ,ain' aA=_�l b o ,
<br />Bin }B = s 8 c G-Iso°=(A+B)
<br />f f4 �y&�¢ ere a—h•� s— (a—c)
<br />pLt, b, a Areae t .�
<br />`33Y.. - i bi b.o sin "
<br />A,' , e. Area' area — —
<br />C� w' = :
<br />, ea a cin B cin C
<br />Ca Area ar
<br />' ! • { ,� 2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance—Slope distance multiplied by the
<br />cosine of the vertical. angle. Thus: slope distance =319.48.
<br />"Lopee Vert angle=5° 10'. From Table, Page ]X. cos 601(V=
<br />'Z e 6"s 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />\ y spo pQ�e Horizontal distance also=Slope distance minus slope
<br />distance times (1—cosine of vertical angle). With the
<br />1 e same figures as in the preceding example; the follow-
<br />" , Horizontal distance ing result is obtained. Cosine 5110'=.9959.1—.9959=.0941.
<br />319.4X.0041=1.31. 319.4-1.31=318.19 ft.
<br />�d When the rise is known, the horizontal distance is approximately:—the slope dist-
<br />"
<br />ce less the square of the rise divided by twice the slope distance. Thus: rise=i4 fL,
<br />C� ope distance=3026 ft. Horizontal distance=99215- a 1 X 14 X8=9028-0.32=302.?$ ft.
<br />7 T MASE IN U.B.A.
<br />a,
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