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<br />TRIGONOMETRIC FORMULtE
<br />1R .
<br />B Bim, Its -as— B
<br />c a c `aZ c -3$`
<br />�
<br />b C A A C� b - C
<br />Right Triangle ' Oblique Triangles
<br />Solution of Right Triangles
<br />a .b-----•- a b e
<br />t i 'For Angle . . sin = , cos = , tan= b ,cot = a , sec = L , cosec =
<br />F Given Required
<br />a, b A, B ;c tA = a T cot B, c = z -F = a j b-
<br />/ an b rt +
<br />—�-
<br />a,c A>B,b sinA= ac=cosB,b=\1(c-}-a.)(r; a)=c�j •tioz
<br />A, a'- B, b, c B=90°—A,-b = a cot A, c=
<br />sin A.
<br />A, b B, t c B=90°—A,a = btan A -,.e= b
<br />1 cos A.
<br />A, c B, a, b B- 90°—A, a = c sin A, b; c cos A,' '
<br />Solution of Oblique - Triangles
<br />j 1 Given Required a sin B
<br />a b,_ e, C b = C = 180°—(A + B), o = asin.0
<br />r sin A sin A
<br />ct
<br />A, a, b B, c, C sin B ='b sin ,
<br />A C = 180°—(A i B) , c =
<br />a sin C,
<br />sin A
<br />a—b) tan A ' 'B
<br />a, b, C, A, I3, c A� B-180°- C, tan ' (A—B)= ( -- c ),
<br />-
<br />` a• sin C
<br />Sin 21.
<br />i� a, b,..c A, B, G sf 2 ,sin,A—, b e
<br />sin:-B='G`'—a)(`�) C-180°
<br />i a, b, c Area- a+ 2+0 area
<br />A, b, e Area arca = b e sin A
<br />i 2
<br />'A, B, C, a Area area = a= sin B sin C
<br />1 �. 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 />{
<br />t5. Vert. angle= 51 10'. From Table• Page IN. cos 50 101= e ass N 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />1 S1o� ��te Horizontal distance also=Slope distance minus slope
<br />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 51 l0'=.9959. 1—.9959=.0041.
<br />3394X.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+slops distance. Thus: rise =14 ft.,
<br />slope distance=302.6 ft Horizontal distance=302.6— 14 X 14
<br />-302.6-032=302.28 ft
<br />2 X 302:6
<br />_ MADE IN U.S. A. '
<br />1 � - mid' .. � •
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