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<br />os TRIGONOMETRIC FORMULAE
<br />B B
<br />c a c a c a
<br />d
<br />AA C
<br />b Cb Cb �
<br />. Right Triangle, .. ; Oblique Triangles
<br />Solution of Right Triangles
<br />a b a b c c
<br />For.Angle A. sin = c , cos = c , tan= b , cot= a , sec = b , cosec =
<br />a
<br />"Given, Required L 2
<br />a,b A,B,c tanA=b=cotB,c= a2+b2=a 1 { az
<br />a, c._ . . A, B, b sin A = a = cos B, b = V (o+a) (c—a) = e 1— ao2
<br />A,.a B, b, c B=90°—A, b = acotA,c= a
<br />sin A.
<br />A;•b•:• B, a, e B=90°—A,a = btan A,a= b
<br />cos A.
<br />'A;'a.' B, a, b B=90°—A,a=esin A,b=ccos A,
<br />Solution of Oblique Triangles
<br />Given Required
<br />a sin B a sin C
<br />A, . B, a b, c, C b = sin A ' C = 180°—(A { B), c = sin A
<br />b sin A a sin C
<br />A, a, b B, e, C sin B = a , G = 180°—(A { B), c = sin A
<br />a, b, C A, B, c A+B=180°= C, tan a (A—B), (a—.b)tan 11(A -}-B),
<br />a + b
<br />a sin C
<br />c =_
<br />• '' sin A
<br />ai b+c V(s_b
<br />a, b, a A, B, C s= 2 ,sin ;A—= be
<br />'
<br />sin aB= `I(s a c ),C=180°—(A+B)
<br />a, by a Area s= 2 a+b-1-c , area = s(s—a s—b) (sc)
<br />A, b, c Areab c sin A
<br />area = 2
<br />a2 sin B sin C
<br />i A, B, C, a Area area = 2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance=Slope distance multiplied by the
<br />icosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />. `arca Vert. angle =5° 101. From Table, Page IX. cos 50 101=
<br />e ass y 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />CoAn�1e Horizontal distance also =Slope distance minus slope
<br />distance times (1—cosine of vertical angle). With the o
<br />same fikures as in the preceding example, the follow -
<br />Horizontal distance ing result is obtained. Cosine 51 101=.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 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 =3026-0.32=302.28 ft.
<br />2 X 302.6
<br />Mune w U. e. A.
<br />A
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