|
TRIGONOMETRIC FORMULAE
<br /> B i 9• B
<br /> <- 7 z�s a
<br /> � a a
<br /> -.."9--rte'
<br /> 4. A AJU
<br /> 15Gy b C b C b , C
<br /> YS O/ o G Right Triangle Oblique Triangles---�
<br /> Solution of Right Triangles
<br /> a b
<br /> For Angle A. sin = ,cos= ,tan= a ,cot= a,sec= , cosec= a
<br /> z � � c c b a
<br /> - ! Ss 3 ;, - x Given Required
<br /> lout ✓ a ! '.z, a, b A, B',c tanA=b= cotBc = a } ' =a 1+
<br /> f
<br /> 0
<br /> sl 3 a, c A. B, b sin A=a=cos B,b=%/(c-I-a c-a =a 1-as
<br /> 4
<br /> 1 '. a B, b, c B=90°-A,b=acotA,c= a
<br /> sin A..
<br /> A, b B, a,.c B=90°-A,a = b tan A,,c=
<br /> cos A. 6a.-4 1 J"
<br /> B, a, b I B=901-A,a =c sin A,b=c cos A,
<br /> ?? r Solution of Oblique Triangles
<br /> "L Ij Given Required --
<br /> �� _ 1, B,a b, c, C b =a sin B C = 180°-(A +B), c = a sin C 7.i'7.
<br /> sin A sin A
<br /> b sin A , a sin C
<br /> A, a, b B, c, C sin B= a ,C= 180 -(A-I-B),c =
<br /> sin A
<br /> �J--17 ah b, C A, B,c A+B=180°-C,tan'(A-B). a-b tan 1(AA+B)
<br /> %� .. c a sin C a i b
<br /> sin A
<br /> 8-6
<br /> b,b, a A, B, C 8=-2 ,sin aA= a s-c
<br /> a �ls-axa-c C-180°-{A i B)
<br /> W
<br /> sinB=
<br /> 6 , ac '
<br /> �g t b, c Area s=a+b ) c
<br /> 2 , area = a(s-a s-
<br /> (y-c
<br /> bcsinA
<br /> A, b, a Area area = G r)14 Z.,�i b
<br /> 2
<br /> a2 sin B sin_C
<br /> }> - A,B,C,a Area
<br /> 2sin Ay"Ls_v q
<br /> REDUCTION TO HORIZONTAL T4 7 y i
<br /> Horizontal distance-Slope distance multiplied by the
<br /> 7.,' ce cos ae of the vertical an¢le.Thus:slope distance-319.4 It.
<br /> p u �ytan d Vert-angle=6°101. From Table,Page IX.cos 6°1N=
<br /> q „ AM Horizontal distanoo=810.4X.9969=91&o9 ft.
<br /> h 1 Angle Horizontal distance also=Slope distance minus l slope distance times(1-cosine of vertical anuie). with the•
<br /> same figures as in the preceding 9'u a¢example,the follow �`
<br /> Horizontal distance inpg result is obtained.Cosine 6°lW=.9969.1-.9969=AkL '
<br /> When the rhiil. tah xfnt�-s1#411 sata�e b-S1&09 tt
<br /> L - anee 1asriae dislded by twicrthe slupeQ atauce:` • mise=}#
<br /> ' v 1 b vt S slope dIatance=a02tit Horizontaldistance=992.E-z xea80a8-0 92x802 29 It. `,z
<br /> MADE IN U.%.A.
<br /> a
<br /> A' ..
<br /> s
<br /> • r
<br /> so
<br /> 0.
<br /> i�
<br /> r
<br />
|