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TRIGONOMETRICFO_RMULIE
<br />�r
<br />B B
<br />-dfc' i c a o a c a
<br />/�:I
<br />� 9��`UB C — b C A b C i
<br />f .
<br />5 7 I �� �� J _ Right Triangle Oblique Triangles r
<br />F
<br />T T' /jj Solution of Right Triangles
<br />a b a b " ql 3 85 y For Angle A. sin = o , cos = a , tan = b , cot = a —,sec= b , cosec = a
<br />`Gillen Required
<br /># , `•- t%
<br />a,b A,B,c tanA=b=cotB,o= a2-{- z=a 1+a2
<br />r �_.- Def II`I•
<br />? . a, a A, B, b sin A =a = cos B, b = V (T+a (c—a) = a J 1
<br />" A,' -a B; b, c B=90°—A, b = a cot A, o= sin A.
<br />y A, _b B, a, c B = 90°—A, a = b'tan A, c =
<br />cos A.
<br />A, c B, a, b B= 90°—A, a = o sin A, b = c cos A,
<br />'O 2 • �� �$? S5� , . j" Solution of Oblique Triangles
<br />Given Required a sin B
<br />A, B,:a b, c, Cb = sin A ' C = 180°-(A + B), c = sin.A
<br />�'P' r�� A, a b B> c C sing= sa A,C= 180°—(A +_B), a = sin A
<br />/1 << a, b, C A, B, c A-FB=180°—.C, tan z (A—B)= (a—b) tan 1'(A+
<br />B).
<br />jasin C a+b
<br />2 S 5 =T
<br />63 ° =sin A
<br />b a A, B, C s = a+b +o — I(s—
<br />a 2 ,sin';A— VI b e
<br />sinaB=�(y—aa�c ,C=180°—(A+B)
<br />a+b+c
<br />r� ati b, c Area s= 2 , area = VS(a—a) (s—)(8-0
<br />3.3
<br />! r� i%�f A, b; c ` Area area = b c sin A
<br />2
<br />A, -Area s
<br />area = a2 sinB sin
<br />C
<br />7 ul
<br />REDUCTION TO HORIZONTAL
<br />? _) 4 Horizontal distance= Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slope distance=319.4Pt.
<br />�• 3v_ �` 1 ta9ce Vert. angle= 50 101. From Table, Page I%. cos 50 10Y=
<br />o ass . y 9959. Horizontal distance=319.4X.9959=318"09 ft.
<br />5 > r��o4 An�1e CG Horizontal distance also=Slope distance minus slope
<br />�-�-•-,p- -distance times (1—cosine of vertical angle). With the
<br />n l� same figures as in the preceding example, the follow-
<br />Horizontal distance ing result is obtained. Cosine 5° 101=.9959.1—.9959=.0041.
<br />a ✓ r /e 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 />tv =�) ante less the square of the rise divided by twice the slope distance. Thus: rise =14 ft.,
<br />i 14X14=
<br />slope distance=302.6 Pt. Horizontal distance=302.6— 302.6--0.32=302.28 ft.
<br />2 X 302.6'
<br />M
<br />MADE IN Y. S. A.
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