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<br /> (, $ _q g_^' TRIGONOMETRIC FORMULIE /
<br /> 4
<br /> 7, 0 3 a a
<br /> b a -b A b a
<br /> Right Triangle a
<br /> Oblique Triangles
<br /> a
<br /> 1-7.7 s Solution of Right Triangles
<br /> For Angla.d. sin =o ,cos= a tan= b ,cot__= a,sec—T, cosec=
<br /> Given 'Required a a
<br /> /,r 4G. �Sa gbd,B,c tanA=b=cotB,c = a2+ Y= a 1 fas
<br /> g �-,s 3 a, a ?:B, b sin A=a =cos B,b- c a o--a --
<br /> A,a B; b, c B=90°-A,b=a cotA,o= sin A. J m
<br /> o , 1
<br /> A, b B,ja,.c B<90°-A,a = btanA,°= b cos A.
<br /> 4 Y3 A,o B, a, b B=900-A,a =c sin A,b= c cos A,
<br /> 3 Solution of Oblique Triangles
<br /> 3 1
<br /> Given Required a sin$
<br /> �!
<br /> 47 -1-- 4- A, B,a b, e, C b= sin A ' 6r-.180°-(A+B), ° = a sin C
<br /> j'
<br /> 0 sr 7,a sin
<br /> D"i I J. .r- 34 bsin A 0 7 d, a, b B,a, C sin B= ,C= 180'-(A�- B)�c = a sin C
<br /> 36 , i { _`��_2 0, a sin A
<br /> 2 . ! 1 C C d 40 7 17 0..b, C. A, B,° A+B=180°-C,tan j(A-B)= a-b)tan i(A+B3
<br /> 5,7 ° =asinC a+ b ,
<br /> ` sin A
<br /> 0. b, 0_. A, B, C a=a+b+0,sin IA= is-b)(s y,
<br /> 94 .� � 2 b° 17—e ,�
<br /> L y
<br /> J / sinB=�(s-aNs-c a-
<br /> _�- -180 A+B
<br /> a+b+
<br /> a, b, ° Area s= 2 , area = s(e--a a— (s—c
<br /> =, 33. o
<br /> . 4 3 ,G L �. S' 9 A, b, c Areaarea = b e sin A
<br /> C
<br /> A,B, ,a Area area =a2 sin B sin C i 3 P
<br /> o 9 7 N o_ 2 sin A
<br /> S JL-1-1-—0 31 it 8 REDUCTION TO HORIZONTAL '
<br /> L Q Q 41 Horizontal distance=Slope distance multiplied by the
<br /> '-40 z cosine of the vertical angle.Thus:slope distance=319.4 ft.
<br /> q i'O 7 ' 7 u 3 �' �— ata�� - Vert angle=b°10'. From Table,Ps¢e iX.cos b°10'=
<br /> Ij ��11 8959. Horizontal distance=319.4X.9959=318.09 ft
<br /> 3 T •g y 's�O� A¢a�e Horizontal distance also=Slope.distance minus slope
<br /> 1 b V �, / 7 `� ,!f y Ve distance times(1—cosine of vertical an9ie). With the
<br /> �1 V same figures as in the preceding example the follow-
<br /> •(/ Horizontal distance in result is obtained.Cosine b°10'=-99 ,1-.9969=.0041.
<br /> 3
<br /> •r is 814X.0041=1.31.319.4-1.31=81"ft
<br /> When the rise is known,the horizontal distance is approkimately:—the slope dist ,
<br /> ante less the square of the rise divided by twice the slope distance. Thus:rise=
<br /> 2Xl4 ft,
<br /> slope distance=309.8 ft Horizontal distance—Me—142�. _ � =
<br /> 90 8
<br /> ' 1,� - MADE IN U.S.A.
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