|
TRIGONOMETRIC FORMUL&
<br /> 3 ti- B B
<br /> a c a ° a
<br /> b Q A b C A b C
<br /> ° '� Jy y,= � • 6 Right Triangle Oblique Triangles
<br /> 7.1 7 Solution of Right Triangles
<br /> For Angle A. sin =a ,cos= b ,tan= a ,cot = b,sec= a. cosec-
<br /> 3
<br /> r� 1 �• a b b
<br /> �i 3-r,/6 Given Required c a a
<br /> a, b A, B,c tan A=b= cotB,c = ay+ s =a 1 } as
<br /> s
<br /> - 7 7 3 9 s a, a A, B, b sin A=a =s cos B,:b=V(c+a c---a =c
<br /> 6 7 A,a B, b, c B=900—A,b =a cot A,a= a
<br /> 3 . 4' o sin A.
<br /> `' -- 7 c b
<br /> � A, b B,a, B=90°—A,a = b tan A,a= U
<br /> ----- 3
<br /> J. 7 y cos A.
<br /> -- - - / A,c B, a, b I B=90°—A,a =a sin A,b=c cos A,
<br /> i - Solution of Oblique Triangles ,
<br /> 7, y Given Required a sin B
<br /> ,j A, A a b, c, C b = ein A ' C= 180°—(A+B),.,s A
<br /> bsinA asin C
<br /> A, a, b B, c, C sin B= a ,C= 180°—(A+B). sin A
<br /> c =
<br /> a, b, C A, B, c A+B=1800—C;tan 3(A—B)= a—b)tan J(A+B).
<br /> a+ b
<br /> a sin C
<br /> sin A
<br /> L r
<br /> 1 ? a, b, o A, B, C s=a+2 ,sin,'A=�B b e—a
<br /> �.. �.
<br /> sin2'B= 18ac �C=180°—(A+B)
<br /> 40.,,. �� d -� a+b+c
<br /> 50.6134.. a, b, c Area a= 2 , area = e
<br /> 38 .6157.78 7 J
<br /> 10.6180.781 b c sin A
<br /> A, b,-c Area area =
<br /> 20.6202.790. a..-, `'-, $
<br /> 80.6225.7954 ` az sin B sin C
<br /> 40.6248.8002 - y A,B,C,a Area area =
<br /> 50.6271.8050 �' .. i , 2 sin A
<br /> y v _ REDUCTION TO HORIZONTAL
<br /> '
<br /> CoenCote. _ � �g�pee o Horizontal dista4ce=Slope distance qqncd by the
<br /> cosine of the vertical angle.Thus:slope =319.4&
<br /> Vertangle=50IW. From Tablpm6ix
<br /> cog,s°119=
<br /> 90Horizontal dietanoe=819.4X.90631&09 ft.
<br /> 0040 A9a1e H60.Horizontal distaaee also=Slope distance minus slope
<br /> 4e distance times(I—cosine of vertical eagle). With the
<br /> g' same figures as in the preeedin example, follow-
<br /> Horizontal distance 1 result is obtained.Cosine 6°1lt=.991911 .0041.
<br /> 4X.0041=1.31.319,4-1,31=81L%ft.
<br /> When the rise is known,time ontrd distanee L approximately.—the slope dist-
<br /> once leas the square of the rhro'divided by twice the slope distance. Thos:rise=14 ft.,
<br /> slope distance=3026 it HorizenW glenogee=303,Ii---b�X'4.-4M6—eJ2-90220 ft.
<br /> 2X3,0246
<br /> am IN U.a.&.
<br />
|