No / ��� t �Sda1 aF a ? TRIGONOMETRIC FORMULYE G I ,1 B B B
<br />a
<br />a —g a c
<br />gidA
<br />b C �b C A C
<br />.. .. i I Right Triangle - Oblique Triangles
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<br />Solution of Right Triangles -
<br />For Angle A. sin = a , cos = c b , tan= a , cot = b , sec = cosec =
<br />c b b a.
<br />( Given Required ab?'a,b A,B,c tan A=b=cotB,e=Vo,2+bz=a 1 { a
<br />`Y as
<br />a, c A, B, b sin A =a ic = cos B, b = \/ (c+a) (c—a) = c
<br />/ A,a:.="B, b, c B=90'=A,b=acotA,c= a
<br />I
<br />sin A.
<br />i A, b,
<br />B, a, c
<br />B = 90°—A, a = b tan A, c = b _
<br />_
<br />cos A.
<br />A, b r
<br />B, it, b I
<br />B = 9.02-,A,.a- c in A, b = c cos A,
<br />Solution of Oblique Triangles
<br />Given
<br />Requireda
<br />sin B
<br />A, B, a
<br />b, e, C
<br />b _
<br />, C = 180°—(A + B), c =
<br />sin A sin A
<br />A, a,'b
<br />B, c C
<br />sin Bb sin A = ,C = 180°—(A (B), c a sin C
<br />=
<br />a sin A
<br />a, b, C
<br />A, B, c
<br />1 (h—b) tan -'a (A+B)
<br />A+B=180 - C, tan z (A—B)=
<br />a + b ,
<br />1
<br />a sin C
<br />_
<br />c sin A
<br />a, b, c
<br />A, B, C
<br />s=a+2+c'sin 'A= -VA a(cs-c
<br />sin aB=�(s-aa(� ),C=180°—(A+B)
<br />a+b-1-c
<br />a, b, a
<br />Area
<br />6= 2 , area = s(s—a s—b)(s—e,
<br />A, b, e,
<br />Area
<br />area = b c sin A
<br />2
<br />sin B sin C
<br />A, B, C, a
<br />Area
<br />area - = —
<br />2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance = Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slope distance=319.4ft.
<br />Vert. anl= 51 101. From Table, PaIX. cos 10 =
<br />e a'StQ�ce
<br />y 9959. Horizontal distance=319.4X. 959= 3 3.09 ft.50
<br />sN A Xe
<br />a Horizontal distance also=Slone distance minus slope
<br />distance (1—cosine With
<br />vc
<br />times of vertical angle). the
<br />distance
<br />same figures as in the preceding example, the follow -
<br />ing result is obtained. Cosine 50 101=.9959.1—.9959=.0041.
<br />,Horizontal
<br />i the is known,
<br />319.4X.0041=1.31.319.4-1.31=319.09 ft.
<br />the horizontal distance is dist-
<br />,When rise approximately:—the slope
<br />ance less the square of the rise divided by twice the slope distance. Thus: rise=14 ft.,
<br />slope distance=3302.6 ft.
<br />Horizontal distance=302.6— 14 X 14 =302.6-0.32=302.28 ft.
<br />2 X 302.6
<br />• MADE IN Y.S.A.
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