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7 rr; - 7
<br />TRIGONOMETRI FOQkI"I.tE "
<br />B L' B
<br />c a c a c
<br />a
<br />�� A b C A�b C A
<br />I Right Triangle Oblique Triangles _
<br />1 Solution of Right Triangles
<br />a b a b c 0
<br />1 For Angle A. sin =c , cos = e , tan = b , cot = ¢ , sec = b , cosec =
<br />Given Required a
<br />T, a, b 11, R ,c tan.11 , b = cot B, c = az —+32 = cs.� 1 +2•
<br />a
<br />a, c A, B, b sin A = cos B, b^= 1' (c -I -a) (o—a) = c i/ I. n m
<br />4) A, a B, b, c B=94°—A, b= a cotA, c= a
<br />sin A.
<br />A, b B, a, c B=94°—A, a= b tan A, e= b
<br />cos A.
<br />A, c B, a, b B=90°—A, a = c sin A, 8 = c cos A,
<br />Solution' of Oblique Triangles
<br />Given Required a sin B a sin C
<br />A, B, a b, c, C b = - , C = 18W.—(A + B), c = sin A
<br />sin A
<br />a s.
<br />A, a, b . B, c, C sin B= b sin A ,C = 130°—(A } C
<br />a 7�), c = insin A
<br />b, C A, B, c A+13=184°—C, tan 2(A --B)_ (a—b) tan r (A. +R), .
<br />_asinC
<br />if c sin 'i
<br />i
<br />h a, b, c.. A-, B, C s-a+2+c,sin:',.9 b(e—c), .
<br />a+b+cac
<br />a, b, •c Area s= 2 , area = ll( --a) (s—b) (,—c
<br />bcsiaA
<br />A, b, c Area area =
<br />2
<br />a! sin B sin C
<br />1 A, B, &,a Area flLe¢-= sin A `
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />cosine of the vertical angle. Tb us: slope distance =319.4 ft.
<br />t3°°e Vert. angle =5' 101. From Table, rage IX. cos 50 lot=
<br />&N, 0; 9959. Horizontal distance -919.4X.9959=318.0%
<br />c�o4e �,Oe a Horizontal distance also =Slope distance minus slope
<br />e t. distance times (1—cosine of vertical ankle). With the
<br />same fignres as i, the preeeding example, the follow-
<br />11orizoatal distance Ing remit is obtained. Cosine 50101=.095U.1 .9059=-0041.
<br />319.4X•01141=1.31. 313.4—].31=318.09 ft.
<br />When the rise is known, the horizontal distance is ar)Proximately:—the slope dist-
<br />ance less the square of the rise divided by twice the slope distance. Thus: rise=l4 ft.,
<br />slope distance=302.6 ft. Horizontal distance=302.0— 1A ,< 14 =302.8—o.32=30228ft.
<br />z X 302.6
<br />�. MADE Ia U. 5, A.
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