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6 TRIGONOMETRIC FORMULIE
<br />4� B
<br />b C b C
<br />0 Right Triangle A� Oblique Triangles
<br />Solution of Right Triangles
<br />L a b a b c
<br />For Angle A, sin = c , cos = e , tan= T, cot = a , sec = b , cosec = —
<br />(- Given Required a a a
<br />r'�.. r r✓2� s� i a,b A,B,c tan A=b= cot B,c= a2 i 2=a 1-I- az
<br />c A, B, b sin A= a= cos B b= c a c— a a2
<br />e Z3) U �� ,.A,a B, b, c B=90°—A,b=acotA,c= sin A.
<br />h t �� C7 A,
<br />b B, a, e B = 90°—A, a = b tan A, c = cos A.
<br />i
<br />X�-2A, a B, a, b B=90°—A, a = c sin A, b = c cosA,
<br />Solution of Oblique Triangles
<br />Given Required a sin B
<br />y�Jl� !� D A' B' a b' c' C b = sin A ' C = 180°—(A -I B), c ='sin C
<br />sin
<br />f
<br />A, a, b B, c, C sin B= b sian A.Q = 180°—(A f B). c = sin A
<br />/ D ° (a—b) tan 2.(A+B)
<br />z - 39 OO : a, b, C A, B, c A -(-B=180 — C, tan �, (A—B)= a + b
<br />'t'0 { _ a sin C
<br />sin A
<br />b, c A, B, C s= 2 ,sin �A= Y . be
<br />4Z02.3? q -«
<br />L
<br />-
<br />;z-8
<br />v i O v L'
<br />Yoz.o9
<br />V• ry
<br />fes• N D
<br />sin;B= Y s a c C=180°—(A+B)
<br />I '
<br />a, b, c Area s = a+ 2 c, area = 1/s(s—as— (s_ c
<br />I ;A, b, c Area be sin A
<br />area = 2
<br />Iaz sin B sin C
<br />i A, B, C, a Area area, = 2 sin A
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance' multiplied by the
<br />cosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />tQOpe Vert. angle =5° 101. From Table, Page IX. cos 50 10'=
<br />ass ro 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />$1o4e Angle a Horizontal distance also=Slone distance minus slope
<br />Ve 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 50 101=.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 />slope distance=3026 ft. Horizontal distance=302.6— 14 X 14 =302.6-0.32=302.28 ft.
<br />_ 2 X 302.6
<br />MADE W V. s. A.
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