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<br />TRIGONOMETRIC FORMULAE
<br />B B B
<br />c a c a a
<br />d A b C A b C
<br />b C
<br />}• \ Right Triangle Oblique Triangles
<br />- Solution of Right Triangles
<br />�l!1 • 1 . .r � , b a b c c
<br />For Angle A.' sin = a e , cos = c ,tan = b ,
<br />cot= a , see= b , cosec = a
<br />Given Required a z
<br />a, b A, B ,c tan A = b = cot B, c = a2 + s = a 1 } a2
<br />s
<br />a,, c A, B,' b sin A = a =cos B, b (o+a) a) (c—a) = c 1— u
<br />A, a B, b, c B=90°—A, b = a cot A, c=
<br />{ 1.
<br />sin A.
<br />b
<br />h j lI A, b B, a, c B=90°—A, a b tan A, c = 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 />!. Given Required
<br />A, A a b, c, C b' = sin A sin A C = 180°=—(A { 'B), c a
<br />=sinA
<br />sin
<br />A
<br />b sin A
<br />-sin C
<br />A, a, b B, c, C sin B0' , C = 180°—(A + B), c = sin A
<br />b, C A, B, c A -}-B=180°— C, ten 1 (A—B)= . (ab) tan 3 (A+B)
<br />,
<br />a + b
<br />a sin C
<br />sin A,
<br />l a+b+c I— Is
<br />s_ ) 8—c
<br />i a, b, c A, B, C 8 = 2 ,sin= ,
<br />be
<br />sin'B= (s—a)(8ac---c), t a c—C=180°—(A+B)
<br />,f }? a, b, c Area s=a+2+c, area =118(8—a
<br />'--A; b, c Area area = b c sin A
<br />2
<br />` aR sin B sin, C
<br />(' A, B, C, a Area area = 2 sin A
<br />REDUCTION TO HORIZONTAL
<br />I Horizontal distance= Slope distance multiplied by the
<br />I cosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />1 tisooe Vert. angle= 50 101. From Table, Page IX. cos 50 30'=
<br />i ass d 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />5,oQ0
<br />,Ne ri
<br />a distance Ho timest(lecosine oflverticalangle).nce 1With nus lthe
<br />�1e same figures as in the preceding example, the follow-
<br />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 />' r When the rise is known, -the horizontal distance is approximately:—the slope dist-
<br />r ___• •-. ance less the square of the rise divided by twice the slope distance. Thus: rise=14 ft.,
<br />slope distance=302.6 ft. Horizontal distance=3026— 14 X 14 =W16-0.32=3=8%
<br />2X=6
<br />MADE IN V. E. A.
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