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ff .
<br />:) / l -' TRIGONOMETRIC FORMUL)E
<br />a
<br />b C f b C
<br />tRight Triangle Oblique Triangles
<br />o a Solution of Right Triangles
<br />f4 — o • ; For Angle A. sin ,= a , cos = b , tan = a ,cot = b , sec = a , cosec =
<br />b a
<br />Given Required
<br />•a 1 z
<br />�a,b A,B,c tanA=b=cotB,c= az } z=a 1�' Qz
<br />,: a ax
<br />L�3 `i� . Q �Z`� a. a �. B, b sin = a = toe B, b = (a I a) —(a --a) 02
<br />�f ( a
<br />� • " r---_'"-'— .l a
<br />A, a B> b, c B = 90°—Ab = a cotes, 0=
<br />' sin A. -
<br />IGGO' ' r A, b B, a, c B = 900—A, a = b -tan A, c = cos A.
<br />d, c B, a, b B = 90°—A, a = c sin A, b = c cos 9 ,
<br />Solution of Oblique Triangles
<br />!. kn y� 1' Given Required _ a sin B a sin C
<br />A, B'a b, c, C b sin A'C=180—(A } B),a= since
<br />b sin a sin C
<br />A' a, b B� C sin B = a , C = 180°—(A B) , a =
<br />`'r"l(-!moi\ sin A
<br />V �— `�1 , (a—b) tan (A+B)
<br />a' b, C A, B, c A+B=180 —C, tan (A—B)= a b '
<br />a sin C +
<br />sin A
<br />a+b+c (s—b)(s—c
<br />a, b, o A, B, C s= 2 'Sin 'A= �I b e '
<br />'r
<br />sin 1B=.`I a c ,C=180°—(d+B).
<br />a+b+c
<br />©,a,;b, c Area 4= 2 , area = a(a—a FS (s—c
<br />A, b_d Area area = b c sin
<br />as sin B sin C
<br />C- —3 ��� 3 1 L. �,B; C,a Area area = 2 sin
<br />J
<br />f 1 a �/' REDUCTION TO HORIZONTAL
<br />N,*'. Horizontal distance= Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slope distance=319.4 ft.
<br />1�ts9e Vert. angle =5° 101. From Table, Page IX. cos 50 10Y= oQe ass y ft
<br />9959. Horizontal distance=319.4X.9959=318.09 .
<br />rgle Horizontal distance also=Slope distance minus slope
<br />A a distance times (1—cosine of vertical angle). With the
<br />Ve same figures as in the preceding example, the follow-
<br />in'
<br />resultis obtained. Cosine 5° 10'=.9959:1—.9959=.0041.
<br />Horizontal distance 319.4X.0041=1.31. 319.4-1.31=318.09 ft.
<br />japproximately
<br />.
<br />'1 1 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=3020 ft. Horizontal dist9_nce=302.6— 14 X 14 =302.6-0-32=302.28 ft.
<br />2 X 302.6
<br />RADE W U. B.k
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