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<br />FA
<br />TRIGONOMETRIC FORMUL B
<br />J73 B B
<br />° a c a c a
<br />A b Cdb Cd
<br />C
<br />Right Triangle Oblique Triangles
<br />Solution of Right Triangles
<br />For Angle A. sin= a , cos = b , tan = a , cot = b , sec = o ; cosec = o
<br />Given Required
<br />a, b d, B ,c tan d = b = cot B, c = as + 2 = a 1 + m2
<br />a
<br />a, c A, B,.b rind = c=cosB,b=\/(c }-a)(c—a) =c J1—a2
<br />A,,a B; b, c B=90°—d, b = acotA, c= a
<br />sin A.
<br />A, b B, a, c B =90'—A, a = b tan A, c = b
<br />cos A. '
<br />A, c B, a, b I B = 90°—d, a = c sin A, b = c cos d,
<br />Solution of Oblique Triangles
<br />Given Required a sin B
<br />A, B, a b, c, C b = , C = 180°—(d ,{ B), c = 'sin C
<br />sin d sin d
<br />A, a, b B, bs
<br />B,.0, C sin B = ain d —{ , C = 180°(d B), c = a sin C
<br />sin d
<br />a, b, C d, B, c A+B=180°— C, tan J (d—B)= (a—b) tan I- (A+B)�
<br />o =
<br />asin C a+b
<br />sin d
<br />a, b, o d, B, C s=a+2+0,sinjA= Vls— b)(C—c
<br />sinaB=V(s alc C=1801-(d+B)
<br />a -{-b+ —
<br />eti b, c ; Area s= 2 ,area
<br />A, b, c Areab c sin d
<br />area = 2
<br />as sin B sin C
<br />B, C, a Area area = 2 sin d
<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 />tan° Vert. angle =5° 101. From Table, Page IX. cos b° 1d=
<br />0 ass / y 9959. Horizontal distance =319.4X.9959=318.09 ft.
<br />Horizontal distance also=Slone distance minus slope
<br />qe ;, distance times (1—cosine of vertical angle). With the
<br />same figures as in the preceding example, the follow -
<br />Horizontal distance ing result is obtained. Cosine 50 10/=.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 />slope distance=302.6 ft. Horizontal distance=302.6— 14 X 14 =302.6-0.32=302.28 ft.
<br />2 X 302.6
<br />KADE M U. S.A.
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