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5
<br />0
<br />97s
<br />a � �
<br />°3 2 i
<br />y. 8z
<br />TRIGONOMETRIC FORMULIE
<br />B B
<br />c a c a c a
<br />d` b CA� b CA b C
<br />R_ ight Triangle Oblique Triangles
<br />+ a Solution of Right Triangles
<br />PFor Angle A. sin=m , cos = b _,tan= a , cot = b —,see= e , cosec =
<br />c cb ab. a
<br />+ Given Required a Ti
<br />a, b A, B ,c tan A = b = cot B, c = a2 + b2 = a ` 1 a
<br />2
<br />a; c A, B, .b sin A = = cos B, b = %1(c+a) (c—a) = c o ff
<br />A, a B, b, c B=90°—A, b= a cotA, c= a
<br />sin A.
<br />b B, a, c B = 90°—A, a = b tan A, c = b
<br />cos A.
<br />e B, a, b B = 90°—A, a = c sin A, b = e cos A,
<br />i Solution of Oblique Triangles '-
<br />Given Required a sin Ba sin C
<br />'A, B,a b, c, C b= s ,C=180,—(A+B)in A,e= sin
<br />b sin A° a sin C
<br />B,o,C sinB= a ,C=180—(A+B),c=
<br />A,a,b sin
<br />b, C A, B, c A.+B=180°— C, tan' (A—B)— (a—b)
<br />tan 2 bA+B)
<br />a sin C +
<br />sin A
<br />i ati b, c A, B, C. s=a+Z+c.sin'A=-\Its— b)(C—c
<br />.�(3--a)(s-c),C=180°—(A+B)
<br />1 {, a+b+c
<br />1 b, c Area 5 = 2 , area —-Vs(s—a) ((s—b) (s—c
<br />A, b, c Area area = bcsin A 2
<br />A, B, C, a Area area = a2 sin B sin Cr
<br />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 />st��°e Vert. angle =5' 101. From Table, Page IX. cos 5° 101=
<br />o'pe a� M 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />rat Pn$1e Horizontal distance also=Slope distance minus slope
<br />Qe a 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—.9959=.0041.
<br />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 />ance less the sgtfare of the rise divided by twice the slope distance. Thus: rise=14 ft.,
<br />slope dlstance=302.6 ft. Horizontal distance=3026— 14 X 14 =302_6-0.32-302.28 ft.
<br />2 X 302.6
<br />NADA IN U. S.
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