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TRIGONOMETRIC FORMULLdE
<br />49,
<br />''A t1 A �.
<br />/ Right Tuangle _ Oblique Triangles
<br />----°s�`�' � SoILA]ori of FlightTriangles
<br />For Angle A. sin cos = ,tan = b ; cot = a , see cosec
<br />Given Required z
<br />B ,c ' tan A = = cot, ; e, = a2 -{ bs = 1
<br />�clo a tya
<br />]ra, c A,. Id b ' sin A—
<br />i A, a B, b; co
<br />acotA,=
<br />�!� L. �• r `` / sin A. ,
<br />A,b B,ae B=—A,a=btanA,o=casA.
<br />A, c ` B, o b-. B—'JO°—A, a — c sin ,-b = c cos A.,
<br />Solution of Oblique Triangles i
<br />Given, Required
<br />a sin B a sin C ` ..
<br />A, ' B, -a ' b, c, C b = C 180' (A . a =. �.
<br />d sin t1 F. A
<br />7 Ff n
<br />— r~t jjj A, a, b' B, c; to sin B= a ,C = 180°—(A i 13), a — a sin C.
<br />sin A
<br />a, b, C_-A.,B,•c A+B=180'—C,tan1(A--B)=(a—b)tan?(A-B)
<br />7' -
<br />Sin C
<br />2
<br />a• ' IL4 _
<br />t � sin .tI
<br />t 1 a, b, o A, B, C s a+0 c,ain ?A=
<br />110e 1 �rl:v— a(
<br />sin `B— + '
<br />'= �+**"`�p �- ,1 � �-(o ��.�:• � ��4. a, b, a Areas = a+� area, _ ' s(s—rr,)
<br />i�r
<br />" A, b c Area - area _ ,b e s:n. A I
<br />2
<br />a' sin B sin C ..
<br />A, B, C,a Area I . area = 2 sirs A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance=Slope distance multipliedby the
<br />1 �l ee cosine of the vertical angle. Th us: slope distance=319.4ft. y.
<br />1 l5tnn Vert angle=5° 101. From Table, Page IX. cos 50 lo'=
<br />1e 9959. Hurizontal'distancc 319.4X.9959-3(8.09 ft. 't'
<br />510 horizontal distance also Slope distance minus slope
<br />distance times (l—cosine of vertical angle). With the
<br />same figures as in the .preceding example, the follow -
<br />Horizontal distanee ing result is obtained. Cosine 5° 10'=.9959.1—.9959=.00.41.
<br />319:4X.00-11=1.31. 319.x4--1.31=318-09
<br />It,
<br />When the rise is known, the harizontal distance is approximately:—the slope dist-
<br />' ance less the square of the rise divided by tw;ce the slope distance. Thus: rise= t4 ft.,
<br />,lope distance=802.61t. Horizontal distance=302.6— 74 X l4 =302.0-0.32=302.28 iL
<br />i •2 X 302.6--
<br />s�npE in;u: s, a
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