|
'•:{ �t✓V2
<br />j'' i TRIGONOMETRIC FORMULAE
<br />Fgs�a =
<br />z
<br />� L tr
<br />3 a,
<br />a! ° a c u
<br />f.A
<br />U
<br />Right Triangle Oblique Triangles
<br />Solution of Right, Triangles
<br />a b b
<br />For Angle A. sin a"= c , cog = c , tsa = ,cot = a ,sec cosec = a
<br />r6ven ,Required b
<br />A, B ,c tan A W = cot B, c = -Va2 { z = a 1 -1 3
<br />b az
<br />a, e A, B,02
<br />!,A.
<br />'A, a B, b, c B=90°—A, b= a cotA, c= a
<br />sin A.
<br />A, b • B, a, c B = 90°—A, a = b taa A, c = b
<br />cos A. i
<br />A, c B, a, b I B = 90°—A, a = c sin A, b = c cos A, a 6
<br />Solution of Oblique Triangles
<br />} Given Required
<br />da sin B a sin C , B, a bc, C b = , C = 180°—(A +B), e
<br />sin A sin A
<br />A; a, b B; c, C sin B= basin A i s C= 180°—(.A } B), c sin A
<br />l
<br />b, C A, B, c A B. ° —(a—b) tan i (A+B) 'g + — a, tan �(�—B}_ a b '
<br />a sin C +
<br />o=
<br />sin A
<br />1 a+b+c1 �(a�)
<br />a, b, a -A, B, C s — 2 ,sin 'A= b G '
<br />sin'B— f(a—aa(.c
<br />yy a �YI
<br />a„ b, o Area s = +Z+G,
<br />A, b, c Areab e sin A
<br />area = 2
<br />e
<br />dy B, C,a Area area = at sin B sin C 2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance —Slope distance multiplied by the
<br />e cosine of the vertical angle. Thus: slope distance=319.4 ft.
<br />o als�26 r Vert. angle= 51101. From Table, Page IX. cos 50 10'=
<br />9959., Horizontal distance=319.4X.9959=318.09 ft.
<br />r>>09 1g a 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 />Horizontal distance _ irg result is obtained. Cosine 5° 101=.9959. 1—.9959=.0041.
<br />319.4X.0041=1.31. 319.41.31=318.09 ft.
<br />When the•rise is known, the horizontal distance is approximately:—the slope dist-
<br />ance less the square of the rise divided by twice the slope distance. Tbus: rise=l4 fL,
<br />alope.distance=302.6It. horizontal distance =3026— 14 X 14 =3W_G--032=30228 ft.
<br />2 X 3026`
<br />- MADE IN U. S. A.
<br />
|