|
_ _ _ �„.%�l.•..• '`" -�.' ",sem"-- 1
<br />_ TRIGONOMETRIC FORMUL)E -
<br />r B n — y' B
<br />tja
<br />;
<br />Right Triangle Oblique Tr angles
<br />3 c' jcl r. Solution -of Right Tria`files c
<br />+' t a b a H&1 c
<br />lFor Angle A. sin= ,cos = c , tnn = b , cot , ¢ ,sec
<br />a'
<br />Given Required
<br />b .1, B ,c tan A = = cot B, c 1 �'
<br />a, c A, B, b sin' A = a = cos B, b
<br />>1�
<br />A, a B, b, c B=90°—A, b= acot_I., csin A..=IA cb B, a, B= 90°—A, a b tan A, c'14
<br />cos A.A, c B, a, b B = 90°—A, a = c sin A, b = c cos A,
<br />Solution of Oblique Triangles - Given Requiredtn asin C
<br />rr'A, B, a b, c, C b — sin� ' C = 1S0°—(A + B), c = sin A
<br />2 t(= b sin A in C
<br />.!'.
<br />A, a,li B, c, C sin B= rt C = 180°—(A -{- B), c = sin A
<br />B)
<br />a—b) tan ' (Af
<br />a, b, C .4, B, c =1 =180°— C, tan ': (A--,—.
<br />a +_b
<br />r c sin A
<br />a, b, c d, B, -C 8 a 2 c in`"4'
<br />—� be
<br />fir,-/nd;r.a,E3 + lv—alts—c)
<br />f �' r�ev�yC�Yj 7.° sin B=C=180°—(AtB)
<br />pea f t r (�y/! s.. r%.. a, b, a -Area s = 2 area
<br />l'
<br />b, ic.. Area _ b c sin A
<br />- area - 2
<br />a"- sin B sin C
<br />B, 'C, a Area area = o
<br />• .. a -4'�,, _ 2 sin A •)
<br />e��� REDUCTION TO HORIZONTAL
<br />J = Horizontal distance= Slope distance multiplied by the
<br />C� cosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />3 / `a�cc Vert. angle =5° 101. From Table, Page IX. cos 50 101=
<br />! e aye .9959. Horizontal distance=319.4X.9959=318.09 ft, .
<br />y.r Shoe ��1c Horizontal distance also—Slope distance minus'slope
<br />Ve t• distance times (t—cosine of vertical angle). With the
<br />�a /•' same figures as in the preceding example, Me follow -
<br />Horizontal distance ing result is obtained. Cosine 51101--9959.1—.9959=.0041.
<br />319.4X.0011=1.31.319.4-1.31=818-09 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. Thus: rise=14 ft.,
<br />jr slope distance=3026 ft. Horizontal distance=302.6— 14 X 14 =302.0-0.32=302.28 ft
<br />. �.., ..►.b. —
<br />2X 302:6'
<br />MADE,IN U. S. A.' •,
<br />
|