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<br />TRIGONOMETRIC FORMULA;
<br />B 11 B
<br />c .• a e a c a
<br />�, A b C A b C I
<br />Right Triangle Oblique Triangles
<br />Solution of Right Triangles '
<br />a b a b c
<br />F+or Angle A. sin = e , cos= , tan= b , cot = , sec = L , cosec =
<br />Ii yF` Given Required a
<br />a, b A, B ,c tan A = b = cot B, c = a ++ by, =
<br />.], B, b sin A = a = cos B, b =1f _(0+-)(o—a) = c
<br />�j A, a B, b, c B=90°—A; b= a cot -4., e a' . J
<br />sin A.
<br />tt i;
<br />1D A, b B, a, e, B = 90°—A, a b tan A, c cos A.
<br />c
<br />A, o B, a, b I B = 900—A, a = c sin A; b = c'cos A,
<br />Solution of Oblique Triangles
<br />Given Required is
<br />y in B
<br />a s
<br />A, B; a b, e, C b = sin .A Sl,'C = 180'—(A -h sin A
<br />b sin •A a sin C
<br />`ef A, a, b B, c,' C sin B- ,C = 180°={A { B), c = sin A
<br />�. 7 r s
<br />S') ) !7 1a ? a; b, C A,. B, a : A { 33=180°= C, tan z (A—�?)= (a—b) tan a QAC B)
<br />f rr 6 asin C aha
<br />sin 11 _
<br />a+b+e
<br />p P_ 'L a, b, e -A, B, C .s—. S ,sin A= b c
<br />. — a ." '
<br />sin
<br />'B—
<br />xB— V,C-184°--- {A.
<br />+Z3)
<br />— S •: . �' , h a b, c Area s 2 ,area = a(,9—a (e—b) (s—c
<br />`� j A; b, -c Area ' b c sin A
<br />`rr. (4. � � area = 2
<br />a, sin Bsin C
<br />,A, B, Ca Area area := 2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance=SIope distance multiplied by the
<br />cosine of the vertical angle. Thns:slopedistance =319.4ft.
<br />y alstal` Vert. angle =5" 101. From Table::Page ]X. cos 5° ld=
<br />9959. Horizontal distance=319.4X:9959=318.09 ft.
<br />�oFe l%v, Horizontal distance also=Slope distance minus slope
<br />VQ . A p' distance times (I—cosine or vertical angle). With the
<br />same figures as in the preceding example, the follow -
<br />Horizontal distance Ing result is obtained. Cosine 5° 10i=.9959. 1—.9859—,0031.
<br />319.4X.0041=1.31. 319.4-1.31=318.09 it.
<br />When the rise is known, the horizontal distance is approximately: --the slope dist-
<br />ance less the square of the,
<br />divided by twice the slope distance. Thus: rise -l4It..
<br />slope djstance=302.6 ft. Horizontal distance=302.6-- 14 X 14 =302.6-0.32=302.28 ft.
<br />;. 2X3026
<br />-� �` MADE IN U. 5,A.
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