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WIN
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<br />TRIGONOMETRIC FORMULzE
<br />B B B
<br />a
<br />AA b C A b 0111
<br />Right Triangle Oblique Triangles %
<br />I; 1 Solution of Right Triangles — -- ;
<br />1` !
<br />a b a b c d
<br />For Angle A. sin: = c ,cos = c ,tan = b ,cot = a ,sec = b , cosec = a
<br />;I Given Required a
<br />y 2 b A"B;c tan A=v= cot B,c= a __ 2=a. 1+. �
<br />a, c A, B;, bsin A = C = cos B, b = V (c-(- a) (o—a) = c 111— e z
<br />1 ! t
<br />( A, a= B, b, c B = 90°—A, b = a cot A, c = a '
<br />sin A.
<br />A, b B, a, c B=90°—A, a= b tau
<br />-� cos A.
<br />A,c. Aa, b I B=90°—A,a=csin A,b=ccos A,
<br />Solution of Oblique Triangles
<br />Given Required
<br />asinB
<br />A, B,a b, q C b=C=180°—(A+B),e-asinC
<br />sinA sin A
<br />b sin A
<br />tti A, a, b I3, c, C sin B = a , C = 180°—(A -F B), c = a sin C
<br />sin A
<br />I a b, C A, B, e A -1-B=180°— C, tan ', (A—B)= a—h) tan z(A+B)
<br />a '
<br />a sin C +
<br />--sin sin A ,
<br />a+b I
<br />a, b, c A, B, C� s— 2 .,sinA` 11 b e
<br />sin iB=1f C=180°—(A+B)
<br />a�bl c
<br />a Areas= 2 s(s—a (s— )(s—c
<br />A, b; c Area fi c sin A
<br />area = 2
<br />I' a' sin B sin C
<br />A, B, C, a Area area = 2 sin A
<br />' REDUCTION TO HORIZONTAL %.
<br />1
<br />Horizontal distance=Slope distance multiplied by the
<br />cosine of tb a vertical angle. Thus: slove distance =319.4 ft.
<br />,St4�ee Vert. angle=� 10'. From Table, Page IX. cos 60 101=
<br />a m 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />slope axe Horizontal distance also —Slope distance minus slope
<br />distance times (1—cosine of vertical angle). With the
<br />same figures as in the preceding example, the follow -
<br />Horizontal distance ing result is obtained. Cosine 5° 101=.9959.1—.9909=.0041.
<br />^19.4X.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=l4 %,
<br />slope distance=302.6 ft. Horizontal distance=30:.6— 14 X 14 =6_0.32=80228 &
<br />2X3028
<br />MADVIN V. -S. A.
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