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<br />TRIGONOMETRIC FORMULAz
<br />is
<br />G a G a C
<br />a
<br />g b C Ab Q !� L U
<br />I Right Trianglc Oblique Triangles
<br />Solution of Right Triangles
<br />For Angle A. sin = Q , cos= o , tan=, h , cot,- a•, sec = b, cosec = a
<br />(liven Required a 5
<br />a, ii A, B ,a tan A =• b = cot B, c a2 } z = a 1 a2
<br />s
<br />a, a A, B, .b ain A = = coe B, b = �/ a�-a (�--a e l -a
<br />a B, k a B=90° -A, b= a cotA, e= a
<br />� sin A.
<br />-A, b Bad B = 90°--A, a = b tan A, e , cos A.
<br />_f A, c B, a'� b I B = 90`--A, a = o sin A, b = e cos A,
<br />a
<br />��` ,��r ///�fj,�p` ��; ' ^ ��/ c{,,•,S l) Solution of Oblique-. Triangles
<br />y ! 1 k ° ! — - 1_ _ ✓ C Given Rcquir'ed
<br />481nB in Q
<br />�`.:, :•t --- A, b, e, b=180' -(A -I -B),
<br />B,a sin
<br />a sin
<br />Alf
<br />wt
<br />I Jr' p b sin A o a ein C
<br />b B, C. C sing= a ,C = 1$D -(A (B), a = sin A
<br />_ ( ) }
<br />a, b, C A, B, o A+B=180'-C, tan }(A --B) o a -b tan ,[A B)'
<br />I
<br />a+b
<br />_ a sin C'
<br />P. a sin R
<br />A, b, c A, 1B, C s- a°,sin jA=
<br />2 N be
<br />sinjB f a -a a -c
<br />V ac
<br />a, b, a Area s - a+2 +a, area
<br />A, 6, c Are ab.a sin A
<br />area 2
<br />l ,, B, C, a Area area - a= sin B sin. Q
<br />r:
<br />2 sin A`
<br />r<+ REDUCTION TO HORIZONTAL
<br />l Horizontal distance=Slope distance multiplied by the i
<br />e cosine of the vertical "ale. Thus: slope distance =319.4 ft
<br />spa Vert. angle=5010Y. From Table, Page IM cos 6' 10r=
<br />m 9959. Horizontal distance=919.4X.9959=318.09 ft
<br />5�o�e q1e Horizontal distance also -Slope distance minus slope
<br />Ve P distance times (1 -cosine of vertical angle). With the '
<br />same figures as in the preceding'example, the follow.
<br />Horizontal distance ing result is obtained. Cosine 6°1N—.9958. 1—.9969=.0041.
<br />1 319.4X.0041=1.31. 919.4-1.91=318.0911
<br />Wheri the rise is known, the horizontal distance is approximately:—the slope dist-
<br />once less the square of the rise divided by twice the slope distance. Thus: rise=14 ft.,
<br />slope distance=3028 ft Horizontal distance -9028— 14 X 14 =$026-0 =30228 : 1
<br />2 X 802.6
<br />i - S
<br />''MAaE.lry U. 9. A. - '
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