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VA
<br />If
<br />LT
<br />4
<br />4—
<br />w
<br />TRICONOMETRIC FORMULtE
<br />B B
<br />d
<br />11� A
<br />b C'A b C
<br />Right Triangle Oblique Triangles r
<br />Solution of Right Tidangle9
<br />a b ,a- b d 0
<br />For -Angle A. -;sin = o , cos = , tan = T" cot = a , scc = b , cosec =
<br />Given Reghired I
<br />a a
<br />a, b A, B ,e tan A Nil &27 a 1 ++ x
<br />a
<br />A B b _ a . _ _ ax
<br />�.+ ¢, 'd sin A cos B; b ; �/ (;mal (c a) = c 1— z
<br />..'1 a
<br />� A, a B, b, c B=9 00 A, b = cr cat A, c=
<br />A,b -IB,a, c
<br />1. Ac 'IB¢
<br />Given
<br />'A, B,a
<br />sin A,
<br />B=9U°---A, a = b tan A, c= L
<br />C4S li, -
<br />B-90° A,a=esinA,b=ccosA,.
<br />Solution of Oblique Triangles
<br />Required a sin B
<br />b, c, C I b = , C = 180°--(A T B), o = asin C
<br />E A, a, b B, c, C
<br />b, Cy _4, B, e
<br />b, d A, B, C
<br />- 1
<br />stn stn A -.
<br />b sir. A a sin C
<br />sin B= ¢ ,C = 180°—(A -- B), e = sig A
<br />_4+B-180°— C, tan ; (A—B)—(4--b) tan 'x (A.+B)
<br />a -i- b
<br />c =
<br />7—
<br />b
<br />—
<br />sin, l
<br />2 sin
<br />sin',',B=��`'' ('— ),C 180°—(A+B)
<br />¢c
<br />a Area +=a+2+c, area = - (s—a} (-s
<br />s—b)
<br />A;'b, c Area b e sin -4
<br />area = 2
<br />¢'- sin B sin C
<br />A, B, -G; a Area area 2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance =Slope distance multiplied by the
<br />cosine of the verticalangle. Thus: slope distance=319.4ft,
<br />�tiari°c Vert. angle 50 10% From Table, Page IX. cos 50 10'=
<br />e dv �' .9959. Horizontal distance t319.4><.9959=318.09 ft.
<br />$0, riq}e Horizontal distance alto= Slope distance minus slope
<br />4e t. A• distance times (1—cosine of vertical angle). With the
<br />same figures as in the preceding example, the follow -
<br />Horizontal distance int; result is obtained. Cosine 511 IO'=.9959 1=.9959=.QMl.
<br />319.4X.6011=1.31. 519.4-1.31=318.03 ft.
<br />When the rise is known, the horizontal distance is approximately:—the slope dist-
<br />nnee less the square of the rise divided by twice the slope distance. Tbus,enise 14 ft.,
<br />"slope distance=3029 ft. Horizontal distance =362.8— 14k14_ 302.6-0;1.2 302.28 ft. <'
<br />2 X SOX
<br />€• - �- - �, MA:]E IM U,ti, A,
<br />r
<br />': A
<br />
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