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TRIGONOMETRIC FORMULiE
<br />B
<br />a
<br />S
<br />33 A b a -4
<br />0 1.
<br />fy 1 A. �Right Triingle Oblique Triangles
<br />Solution of Right Triangles
<br />15
<br />s C
<br />A., sin
<br />• For Angle cosec
<br />jD r
<br />I C CO tan= cut sec
<br />a a
<br />Given 'Required
<br />+
<br />-Va2 +
<br />a, B,i tan A Cot 6 a
<br />7azA,
<br />�j.
<br />7 a, 0 -4, B, b sin A cos B; b. = \/C+ a) (5--a) = e,
<br />02
<br />A, a B, bl. e B=90°—A, b a cotA, c a
<br />sin A.
<br />D, A, B, a,cB 90'--4, a buin A,
<br />b
<br />. '
<br />cc
<br />.7 A, c a, B 90'—,A, a 8
<br />A
<br />C sin A, b r co
<br />'s
<br />A
<br />VScIlution of Oblique' Triangles
<br />x.
<br />Given —:,Re4uired asin Basin C
<br />A, B, a C 180'—(A + B),
<br />sin A sin A
<br />b sin A a.
<br />sin C
<br />4 - 1 .-D A, a, -b- :Bj C,' C sin B= C= 180°—(A
<br />a sin A
<br />a, b, C A, B, o A+B=180'— C, tan tan (A+B)
<br />a + b
<br />+a4
<br />a sin C
<br />0 T C) sin A L 9
<br />A, B, C. s=a+b+ 2
<br />a, in -4 be
<br />2 r
<br />T. 77C)
<br />9 -7 5' a
<br />a, b' c -r.Aren 2 rren
<br />0
<br />.S4
<br />sin A
<br />-"3-- A, b, o-, .Area b '* area =5 5 25 7 :3 '71 -5
<br />2
<br />t a2 sin B sin C
<br />."A B, 6, a, Area area '2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance =Slope distance multiplied' bylbe
<br />cosine of the vertical angle. ope distance =319.4 ft.
<br />S,
<br />V.- e:c� Thus:sl Vert. anffle�51 101. From Table, Page Icos 50.10Y=
<br />0 e 41 .9959. Ilorizontaldi§tance-319.4X.9059=318.Ogft.
<br />"7 SN t,,,0� dNe -4 Horizontal rizontal distance also= Slope distance minus slope
<br />e V . distance times (1—cosine of vertical angle). With the
<br />PRUIC figures as in the preceding example, the follow -
<br />Horizontal disto-nw lm,, result is obtained. Cosine 5°]0'=.99y9.1—.9959=.0041.
<br />319.4X.0041=1.31. 319.4-1.31=318.09 ft.
<br />i Whentherisei s known, the horizontal distance is approximately:—the slope dist-
<br />-6 p
<br />ance less the square of the rise divided by twice the slope distance. Thus: rise=14 ft.,
<br />slope distance=302.6ft. Ilorizontal distance=302.6— 14 X ]4 =
<br />2 X 803.6302.6 . —0-32=302.28 ft.
<br />MADE 18 U. S. A.
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