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<br />TRIGONOMETRIC FORMULfE
<br />B R B
<br />c a ° a c a
<br />A
<br />AA
<br />b CA b C b A.0
<br />,(� { Right Triangle Oblique Triangles
<br />f Solution of Right Triangles
<br />I.
<br />For Angle A, sin = a , cos = b —,tan= a , cot = —,see see_= C , cosec = a
<br />c c b a b- a
<br />'I I Given Required z
<br />a, b •-A, B.,c tap A = b cot B, c = Val + 51 = a,\
<br />1 { b
<br />a%
<br />a, c A, B, b 02
<br />.t A, a B, b, c B=90°—A, b= acotA,c= a
<br />sin A.
<br />A, b B, a;" c- B = 90'—A, a = b tan A, e = b
<br />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 _ a sin B o a sin C
<br />A, ,B, a b, c, C b sin A ' C = 180'—(A + B), c = sin A
<br />b sin A a sin C
<br />A, a, b B; e, C sin B = a ,C = 1800—(A + B), c = sin A
<br />a; b, C; A, B, c A+B=180°— C, tan ; (A—B)= (a -b) tan ? (A �B).
<br />a+b
<br />_asin C
<br />c sin A
<br />I a, bi c A, B, C s=a+�+c sin 12A= -\l b�� °)
<br />sin B=alo c) C=180'—(A+B)
<br />_
<br />a, b, a Area s=a-1--2+c, area
<br />A, b, e Areaarea' = b c sin A.
<br />2
<br />A, B; Caz sin B sin 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 />Star°e Vert. angle -6010'. From Table, Page IX. cos 50 10/=
<br />e 0 ti 9959.' Horizontal distance=319.4X.9959=313.09 ft.
<br />slob Angle Horizontal distance also=Slope distance minus slope
<br />e",
<br />,a 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 10'=,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. Horizontal distance=302.6— 14 X 14 =302.6-0.32=302.28 ft.
<br />2 X 302.6
<br />MADE IN U. S. A.
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