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6 3 TRIGONOMETRIC FCRMULIE
<br /> y 7.a r/ B B B
<br /> /pv/ .7 a a c a c a
<br /> a b' C A�b C A b 1 C
<br /> o - f
<br /> g z b _t- ) j Right Triangle Oblique Triangles
<br /> 13 s 3 -� ti G o y n Solution of Right Triangles
<br /> a For Angle d, sin =c.,cos= a—,tan=
<br /> b,cot = a,sec b, cosec= o
<br /> Z l'�• Given Btpuired a
<br /> r ? � a, b d,B,c tanA=b= cotB,c = aa+ z = a 1 +z
<br /> g 3 > / a az
<br /> I L: f / 3 a, c A B, b sin A=a=cos B,b=�/(a I a (a—a)=c'11—
<br /> Z A,a B, b, o B=90 —A,b =acotA,c= sin A.
<br /> 3, e • 7. 9 3 A,b $a, e B=90°—A,a = b tan A,c= b
<br /> cos A.
<br /> 3. 3 7 // ?.1 1 +1<. B,a, b I B=90°—A,a=o sin A,b=c cos A,
<br /> e,3 7 G i „., Solution of Oblique Triangles
<br /> liteeautrea a sin B 'sin C
<br /> C b sin A ' C= 180°—(A I B), a = sin A
<br /> b sin A a sin C
<br /> 3 7 5? . / /3. 7 z A, a, 4µ B,a, C sin B= a ,C=180°—(A t B),a = sin A
<br /> n 1 (a—b)tan
<br /> C A,B, a A♦B=180 —C,tan a(A—B)— a b
<br /> , /ug, t
<br /> LS °' ' i a =a sin C
<br /> sin A
<br /> b, a A, B, C a=a+2+o,sin A= is-b)(,,—_c),
<br /> y
<br /> (s—a)(S—),
<br /> 3 G 7 ,.,w sin'4B=� C=180°—(A i B)
<br /> as
<br /> S•3 t a q, 3 > a.,b c 4;ses s=a+b+c, area
<br /> 2
<br /> A, b, c Area
<br /> 2 area bosinA
<br /> 2
<br /> 3 A az sin B sin C
<br /> ,B,C,a Area area 2 sin A
<br /> REDUCTION TO HORIZONTAL
<br /> y-------- Horizontal distance=Slope distance multiplied by the
<br /> Y 3 e cosine of the vertical angle.Thus:slope distance=919.4 ft.
<br /> /4",; s5
<br /> _ .. //-LZ c? e at5tQ9c a .998� Horizontal distance Table,14 .8!59 8e 3 8.09 ftb°llY
<br /> $1aQ Arg'Ie Horizontal distance also=Slope distance minus slope.
<br /> -4e distance times(1—cosine of vertical angle). With the
<br /> same figures as in the preceding example,the follow-
<br /> __ j t 3 1:L Horizontal distance ingresult is obtained.Cosine 6°10'=.9959.1—.8959=.0041
<br /> 319.4X.0041=1.31.319.4—l.31=31&09 ft.
<br /> When the rise is known,the hortgontal distance is approximately:—the slope dist-
<br /> __ ante less the square of the rise divid6d by twice the aloes distance. Thus:rise=14 ft,
<br /> slope distance=302.6 ft. Horizontal cgstame-302.6—M X 14=302.6-0.32=3a26 ft,
<br /> C i 2 X 302.8
<br /> cone is U.S.A.
<br /> ; 1J' 3G
<br /> l
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