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V C Cry Y` 1 G1`v G� J -c 0.44
<br />' TRIGONOMETRIC FORMULIE y
<br />B B B
<br />c a c a c a
<br />_ b _ C g�—b G'
<br />1 Right Triangle Oblique Triangles
<br />V Solution of Right Triangles {,
<br />Ta b a b a a
<br />'For Angle A. sin = , cos= , tan= , cot = , sec = , Cosec =
<br />C c b a b a 1#.7''
<br />Given Required
<br />a, b A, B ,e, tan A=cot B, c = a2 = a 1 {- Ta:
<br />a
<br />a A, B, b stn A = d = cos B, b = V (c_+a) (a—a) = a � l ^ az i
<br />c o
<br />` A, a B, 'b, c B=90°—A, b = a cotA, c—
<br />sin A-.
<br />A, b B, a, c B = 90°—A, a = b tan A, o = b }`
<br />cos A.
<br />A, a B, a, b 1 B =90'—A, a = o sin A, 6= e cos A,
<br />.r� Solution of Oblique Triangles L
<br />Given, Required _ a sin Basin C
<br />t
<br />i� A, B,a b, c, C b 6inA'_C=180°—(A { B},e= snA_4.
<br />j b sin Aa sin C r, •;
<br />A, a, b B, e, C sin B= a ,C = 180,_ (A -{- B), o = sin A
<br />a, b, C A, B, o A+B=180°-- C, tan 3Y (A—B)= (a—b) tan ? (A A+B)
<br />a+b
<br />1 c=
<br />a sin C%
<br />sin A
<br />a b c A, B, C s= a} b} a
<br />1 2 ,sin aA
<br />V �
<br />sin2B=u(e ° C=180°—(A+B) •
<br />:-
<br />t -
<br />a I a
<br />1
<br />b, a _ Arca s— 2
<br />b, a Area area = i5
<br />c sin A ;
<br />2
<br />L - . a2 sin B sin C °
<br />B, C, a - Area area =
<br />2 sin A
<br />REDUCTION TO HORIZONTAL {
<br />Horizontal distance= Slope distance multipIied by the
<br />eQ cosine of the veoicalangle. Thus: slope distance =319.4 ft. �.
<br />Slsta� N Vert. angle=5 10. From Table, Page IX. cos 5" 10'=
<br />1 oe.!2
<br />X59. Horizontal distance=319.4X.9959=318.09 it.
<br />SNo
<br />�pg1ei
<br />- k Horizontal distance also=Slope distance minus slope .-
<br />tie t distance times (1—cosine of vertical angle). With the e
<br />same figures as in the preceding example, the follow- -7.
<br />Horizontal distance ing result is obtained. Cosine 51 101=.9959. 1—.9959=.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 />nee less the square of the rise divided by twice the slope distance. Thus: rise=l4 ft., 466
<br />ope distance=802.& ft. Horizontal distance=302.6— 14 X 14 =302.6-0.32=302.28 ft. I
<br />2X.4 02 6„
<br />... - . :-77 t _ -MADE IN a. B. A.
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