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TRIGONOMETRIC FORMULA
<br />1T3 B B
<br />44 c. a c a c
<br />r A rJ A / a
<br />Gr b C b C
<br />Right Triangle
<br />Oblique Triangles
<br />;..' 'Solution of Right Triangles
<br />For Angle A.
<br />a, b a b c a
<br />sn =
<br />i
<br />cos =
<br />e ' c tan= b , cot = a , sec = b , cosec =
<br />Given
<br />+' a,b
<br />Required
<br />A,B,c
<br />a
<br />tan A=a—b=cotB,c= a2+32=a 1+ a2
<br />J
<br />�. i . • a, c
<br />A, "B;: b
<br />sin A = o = cos B, b = \/(c+a) (c—a) = c 1— a'
<br />0
<br />A, w
<br />B, b, c.
<br />B=90°—A, b-= a cot A, c= a "
<br />sin A.
<br />A, b
<br />{
<br />B,, c
<br />b
<br />B = 90°=A, a = b tan A, c =
<br />i
<br />r
<br />cos A.
<br />A, c
<br />B, a, b
<br />B = 90°—A, a = c sin A, b = e cos A,
<br />1 Solution of Oblique Triangles
<br />Given
<br />A, B, a
<br />Required
<br />b, c, C
<br />b=as in B
<br />' C = 180°—(A + B), c = asin C
<br />sin, A - sin A
<br />A;' a,, b
<br />B, c, C
<br />b sin A
<br />sin B = , C = 180°—(A + B), c =
<br />a sin A
<br />' a, b, C
<br />d, B, c
<br />A -{-B=180 — C, tan , (A—B)= (a—b) tan $ (A+B)
<br />a + b '
<br />a sin C
<br />}
<br />c=
<br />sin A
<br />a, b, a
<br />A, B; C
<br />s=a+b +0, ,in 1A'=�1(s—b)s—c
<br />2 V be '.
<br />sinzB=-,I(s—a)(s—c ,C=180°—(A+B) '.
<br />V ac
<br />;..
<br />a, b, c
<br />Area
<br />a+b+c
<br />S= 2 ,area = s (s—a S—F) (s --C)
<br />�r
<br />A, b, c
<br />Area
<br />b c sin A
<br />area =
<br />2"
<br />e(, A, B, C; a
<br />Area
<br />aQ sin B sin C
<br />area = • 2 sin A
<br />REDUCTION TO HORIZONTAL
<br />'
<br />Horizontal distance= Slope distance multiplied by the
<br />cosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />j a�5ta�pe
<br />Vert. angle=50 lot. From Table, Page IX. cos 5° 101=
<br />$� ope
<br />9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />M
<br />a Horizontal distance also=Slope distance minus slope
<br />Arg1e
<br />)' Ve .
<br />distance times (1—cosine of vertical angle). With the
<br />same figures as in the preceding example, the follow -
<br />Horizontal distance
<br />ing result is obtained. Cosine 51 101=.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=302.6 ft.
<br />Horizontal distance=302.6— 14 X 14 =302.6—O.'32=302.28 ft,
<br />—
<br />2 X 302.6 _
<br />-
<br />WADE IN U. 8. A.
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