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TRIGONOMETRIC F'ORMUL.E
<br />B
<br />a c a a a
<br />... t� A A �.
<br />? Z c- b CbOblique
<br />1
<br />Right Ttia le Ohli ue Triangles . Solution of Right Triangles
<br />1 l `': f For Angle A. sin cot.= h , sec = c , cosec = a
<br />a b a
<br />Given Required
<br />2
<br />a; b A, ,B',a tan A = b = cot B; c — as + z = a 1 -I- Q
<br />z
<br />'.
<br />r �� � � �� � � 2 � . ..,�-• 1 . .� �-� �g, --B, L
<br />a
<br />A. a,k ; B, b, c B = 900—A, b = a cotA, a sin A.
<br />�..C;00R— A,"6 B, u, c B=90°—A,a = btanA,e= b
<br />— f A T . cos A.
<br />\ A,c B,a, b B-90°—A,a=.esinA,b=ecosA,
<br />coe a Solution of Oblique Triangles
<br />(liven, Required
<br />a sin
<br />A, B a b; e, C b = sia f = 180°--(A + B), e = sin A
<br />b sin A c_ asin C
<br />A, a, b B, c, C sin B= a , C = 180 (A -I- B) o = sin A
<br />aA,. B, A+B-180°— C, tan —(a—b) a lbA+B
<br />1jb, C +)
<br />asin C
<br />sin A
<br />b, c A, B, G s—a+Z+a,sin 7A—
<br />— —
<br />sin JB =�(a � c—c) C=180°— (A+B)
<br />ti:a j
<br />'� a, b, a Area s a+2+a, area = s(a—a s—
<br />W
<br />A, b, c Arca b sin A
<br />area = 2
<br />CN
<br />Co= sin B sin C
<br />ox _ A, B, -.C, a Area area = — 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 tL
<br />i a�5�Q4ce Vert. angle =60 10'. From Table, Page IX. cos 51 lot=
<br />9858. Horizontal distance=319.4X.9959=318.09 fL
<br />Spvo aq'1e 2 Horizontal distance also=Slope distance minus slope
<br />0 A distance times (1 --cosine of vertical angle). With the
<br />same figures as in the preceding example, the follow-
<br />/ , 3 ( I Horizontal distance ing result is obtained. Cosine 51 101=.9959.1—,9859=.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 />'- snee less the square of the rise divided by twice the slope distance. Thus: rise=l41L.
<br />slope distance=302e ft. Horizontal distance=302.8— 14 X 14 =3026-0.32=302-28 ft.
<br />2 X 302.6
<br />1 - MADE IN V. e. A.
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