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7,7
<br />TRIGONOMETRIC FORMULIE
<br />B
<br />j�c a " a c a d -A b Cb CA C
<br />b
<br />I Right Triangle Oblique Triangles .
<br />Solution of Right Triangles
<br />c c
<br />For Angle A. sin = a c ,cos = b c ,tan = a b b ,cot = a ,sec cosec = a
<br />�a x
<br />Given Required
<br />b A, B ,c tan A = b = cot B, c = ax + bx = a 1 a
<br />{ x
<br />a, c A, B, b sin A = a = cos B, b = c a c—a
<br />a �(� )( )=c�l—ax
<br />Qs
<br />A, a B, b, c B=90°—A, b= a cotA, c= a
<br />sin A.
<br />A, b B, a, c B = 90°—A, a = b tan A -, c = b
<br />cos A.
<br />A, c B, a, b B = 90°—A, a = c sin A, b = c cos A,
<br />Solution of Oblique Triangles
<br />Given Required
<br />A, B, a b, c, C b = a sin B C = 180°—(A + B), c = a sin C
<br />sin A sin A
<br />b sin A
<br />r A, a, b B, c, C sin B= a ,C = 180°—(A B), c = a sin C
<br />sin A
<br />1
<br />a, b, G A, B, c A -}-B=180 — C, tan -s (A—B)= (aA) tan (A+R) ,
<br />ab
<br />a sin C +
<br />c=
<br />sin A
<br />a, b, c A, B, C s=a+b+c,,in 'A= Y(s bc(—c '
<br />+' sin 2,B= I(s—a)(s_c ),C=180°—(A-t-B)
<br />a+b+c �I
<br />a, b, c Area s= 2 , area = s(s—a) (s—b) (s—e
<br />A, b,.c Area area = bcsin A 2
<br />ax sin B sin C
<br />A, B, C, a Area area = 2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />t�'ce Vert. angle= 60 101. From Table, Page IX. cos 50 101=
<br />e ass y 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />i sop.1'n,c
<br />distance ttimest(lcco —cosine oflvertcal angle).istance 1Withlthe
<br />el same figures as in the preceding example, the follow -
<br />Horizontal distance ing result is obtained. Cosine 50 101=.9959. 1—.9959=.0041.
<br />319.4X.0041=1.31-319.4-1.31=318.09 ft.
<br />i 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=302.6— 14 X 14 =302.6-0.32=302.28 M
<br />2 X 302.6
<br />wroe IN V. s, ti
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