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<br />It a Lao G
<br />k 3/3g 3
<br />7 4,
<br />37q 5
<br />110 a 3 --
<br />i
<br />G
<br />n
<br />` a
<br />d3 _
<br />b 6 5 v
<br />99
<br />3
<br />TRIGONOMETRIC FORMULtE -t
<br />b C, A�6 C/ A C
<br />Right Triangle Oblique Triangles
<br />Solution of Right Triangles
<br />1 � ,
<br />i { ab a / b c a
<br />+ or ngle A. sin= c ,cos = , tan = b ,cot = a ,sec = b , cosec = a
<br />I i
<br />a GfKen Required a a
<br />A, B ,c tan A = b = cot B, c a2 + 2=a 1 T a2
<br />1 s
<br />a, A, I3, b sin A = = cos B, b =V (c+a) (e --a) = c 1— 02
<br />A, a B, b, c B=90°—A, b= a cotA, c= a
<br />sin A.
<br />.
<br />A, b B, a, c B=90'—A, a = b tan A, c b
<br />= cos A.
<br />�JA
<br />B, a, b B=90°—A,a = csinA, b= ccosA,
<br />Solution of Oblique Triangles
<br />Given Required
<br />A, B, a b, c, C b = a sin B C = 180°—(A -1- B), c = a sin C .
<br />sin A sin A
<br />b sin A a sin C
<br />A, a,'b B, c, C sing= a ,C= 180°—(A.1 B),c = sin A
<br />(a—b) tan z (A +B)
<br />a, b, C A, B, c A+B=180 -- C, tan ? (A—B)— a + b ,
<br />a sin C '
<br />� G =
<br />sin A
<br />a+b -F c
<br />o, b, c A, B, C s= 2 ,sin;A= be
<br />�V ac
<br />1a+b+c
<br />a, b, c Area s= 2 , area=Vs(8—a) (s— (s --c)
<br />bosinA
<br />it A, b, 'c Area area = . 2
<br />1 a2 sin B sin C
<br />j A, B, 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 />511101.
<br />8�St9oee 9959. Horizontal distance= 19.4� From X 9959 318.09 ftIX. cos5° 10
<br />t�N6Qe Arg'Ne 0 Horizontal distance also=Slope distance minus slope
<br />Ve 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 50 101=.9959.1—.9959=.0041.
<br />i 319.4X.0041=1.31. 319.4-1.31=318.09 ft.
<br />When the rise is known, the horizontal distance is approximately:—tbe slope dist-
<br />ance less the square of the rise divided by twice the slope distance. Thus: rise=l4 ft,
<br />—
<br />slope distance=302.8 ft. Horizontal distance=3028— 14 X 14 —3028--0.32=302.28 it
<br />2 X 302.6
<br />K4E Ui U. G. A, 4.
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