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<br />TRIGONOMETRIC. FORMULIE
<br />539,63,.
<br />B B
<br />it°O3 U 26° a c a c a
<br />0 2600
<br />b CA�b
<br />Right Triangle Oblique Triangles
<br />Solution of Right Triangles
<br />a b a b
<br />;I !
<br />33 / � For Angle A. sin = . ,cos = c ,tan = b." = a ,sec = b , cosec = a
<br />3 Given Required
<br />`' J ', L Z., \ • j 0 a, b A, B ,c tan A = a—b =cotB, c = ' Tz -1- s = a 1 } a2
<br />Z Zs a, c A, B,.b sin d._ �=cosB,b=�(o a)(c—a) =c l—ai
<br />A, a B, b, c B=90°—A, b= a cotA, c= a
<br />sin A.
<br />/0°47' b
<br />Z
<br />`i 3° p 3 6 \ A, .b B, a, c B = 90°—A, a = b tan A, c =
<br />p / °
<br />7. .1ecos A.
<br />• ! /\�'! 7s \ / - §3 i '\ } A, c B, a, b I B = 900—A, a = c sin A, b.= c cos A,
<br />Solution of Oblique Triangles
<br />s Given Required a sin B
<br />A, B, a b, c, C b = , C = 180°—(A + B) , c = a ein C
<br />47 sin A sin A
<br />b sin A a sin C
<br />3s \ 1� A, a, b B, q C sin B= ,C= 180'—(A+B),c =
<br />sin A
<br />a, b, C A, B, c A+B=180°— C, tan ; (A—B)= (a—b) tan 2 (A f B)I
<br />k, c a+b
<br />a sin C.
<br />{l - C.i 1% �. Q • „/ / ' V ,Q % sin A -
<br />1 b, e A, B, C s=a+2+c,sin '-,A=�(s .b(s—c
<br />sin'B= C=180°—(A+B)
<br />a, b, c Area s—a+b+c, area=11s(s—a
<br />A, b, c Area area = b e sin A
<br />30 L„�co2rj 2 o
<br />sin B sin C ^ nl
<br />A, B, C, a Area area = 2 sin A
<br />M V
<br />REDUCTION TO HORIZONTAL
<br />_ ��; -- ✓ 3 7 S� Horizontal distance= Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />ass*ar°e H Vert. angle= 5° 101. From Table, Page IX. cos 51 101=
<br />( 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />�,op e t. Anse a
<br />Horizontal ctimest(1 a cosine of also=S Vertical angle).e distance With slopenus te
<br />V same figures as in the preceding example, the follow -
<br />Horizontal distance ing result is obtained. Cosine 50 101=.9959.1—.9959=.0041.
<br />319.4X.0041=1.31.319.4-1.31=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. Thus: rise=14 ft.,
<br />C slope distance=302.6 ft. Horizontal distance=302.6— 14 X 14 =
<br />✓✓ �� 2 X 302.6 302.6-0.32=30128 28 ft
<br />` MADE IN U. B. A.
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