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t
<br />f TRIGONOMETRIC FORMUL&
<br />B B B
<br />c a c a c a
<br />d
<br />AA
<br />b C�b Cb q
<br />Right Triangle Oblique Triangles
<br />Solution of Right Triangles
<br />For Angle A. sin= a c , cos = b tan = a b c c ' b cot = a ,sec = b, cosec =
<br />a
<br />Given Required
<br />a,b A,B,c tanA=b=cotB,c= as+ a=a 1+as
<br />a
<br />a, c A, A b sin A = = cos B, b = V (c+a (c—a) = c J 1— p
<br />A, a B, b, c B = 90°—A, b = a cotA, c = sin A.
<br />� b
<br />1 ( A, b B, a, c B = 90°—A, a = b tan A, c =
<br />II 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 ein B 0_ 180°—(A + B), c� a sin C
<br />sin A ' sin A
<br />j1 b sin A a sin C
<br />f A, a, b B, c, C sin B = a , C = 180°—(A + B), c = sin A
<br />.1
<br />` cb b, C A, B, c A+B=180°-0, tan i (A—B)=(a-b) tan jL (A+B)�
<br />a + b
<br />—
<br />a sin C
<br />-
<br />sin A
<br />a, b, c A, B, Cs=a+2+c,sin;A= V s b
<br />sin;B=ae ° ,C=180°—(A+B)
<br />a, b, c Area 8=a+2+c, area = s(s—a s— )(s—c
<br />A, b, c Area area = b c si A
<br />} as 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 =319.4N,
<br />tQo°e Vert. angle= 50 101. From Table, Page IX, cos b° 10t=.�
<br />oPe ass CD 9959. Horizontal distance=319.4X.9959=318.09 ft
<br />S, A�TT
<br />�,e
<br />Horizontal
<br />stance timest(1-cosine ofverticalangle) 1Withlthe
<br />�1e 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.0011=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— 14 X 14 =302.6-0.32=30228 ft.
<br />2 X 302.6
<br />MADE IN U. B. A.
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