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<br />TRIGONOMETRIC FORMULIE �D
<br />c a c.
<br />a
<br />iZ�wv�� to Al. c t
<br />L p S' - Right Triangle Oblique Triangles
<br />f
<br />/ Solution of Right Triangles
<br />g a. b a b c c
<br />{ 7 4 FocAn le d. sin = c ,cos= c , tan= b , cot'= a, sec = L, cosec.= a
<br />p I Given, Required
<br />-,4b i Z
<br />a;, b• A, B,c tan ==cotB,c= a2+bz=a{az
<br />a
<br />A,B,b sind=G=cosB,b=�(c1a)(c—a)=c�1—a'
<br />I G;1 a
<br />Ov4 o ` '`. A,a B; b, c B=90°—A,b=acotA,c— sin A.
<br />0/ 4 ;
<br />o¢ 00Zy A, b B, a, c ` B=90* —A, a = b tan A, c = b
<br />cos A.
<br />I• i 5"U A, c B, a, b, B'= 90°—A, a = c sin A, b = c cos A,
<br />U 3' 1 y Solution of Oblique Triangles
<br />$ Given Required
<br />�p
<br />47-- �'° .3 S ''A, B,:a b, c, C b = a sin B C = 180°—(A + B), c
<br />4 ,�S 1.. , sin A ' sin A
<br />U �7i yah i� bsin A asinC
<br />y d �. A, 'Cil b B, c, C sin B = a , C = 180°—(A + B) , c = siri A
<br />i ti i, p
<br />J p bto O� '� a, b, C A, B, c A+B=180°— C, tan s (A=B)= (a—b) tan z (A } B)�
<br />S / ✓ _asin0 a+
<br />O o c sin
<br />bi f sv 9 , a+b+c`. a
<br />1 G a, b, a A, B, C s.= 2 ,stn 2- N b e ,
<br />30u 3 3S 3 Z3L \, sin. aB=`I(s-aa)(c ),C=180°—(A+B)
<br />z
<br />uU b e Area s= a,+b+c area = s s—a s— s—c
<br />13Ij� d, b, c Area area = b2 s2 A
<br />I. a sin B sin C
<br />� � M A; B, C, a Area area = 2 sin A
<br />REDUCTION TO HORIZONTAL
<br />M Horizontal distance= Slope distance multiplied by the
<br />--- cosine ofthe vertical angle.�t'hus:slope distance =319.4ft.
<br />�ao9e Vert. angle=51 10. From Table, Page IX. cos 50 101=
<br />o ass y9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />le Horizontal distance also=Slope distance minus slope
<br />'
<br />Iva
<br />a distance times (1—cosine of vertical angle). With the
<br />41 vc same figures as in the preceding example, the follow -
<br />Horizontal distance ing result is obtained. Cosine 51 10l=.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 i§ approximately:—the slope dist
<br />' ---- ante less the square of the rise divided by twice the slope distance. Thus: rise =14 ft.,
<br />slope distance=302.6 ft. Horizontal distance=3026— 14 X 14 =3026-0.32=302.28 ft.
<br />2X3026
<br />MACE Ia U.S.A.
<br />A
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