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TRIGONOMETRIC FORh1UL1E
<br />B
<br />a c a e a
<br />•-A,=-.: b C A^ b C A b C
<br />-- �j � 1 � -
<br />Right Triangle Oblique Wangles
<br />Right Triangles
<br />So.lutiori''of
<br />b b
<br />r
<br />_
<br />2 a c c
<br />For Angle A. sin = cos= , tan= , cot = a. sec = b, cosec =
<br />c c a
<br />- -- -
<br />Giben
<br />a,b
<br />Required
<br />A,'B,c
<br />tanA==cotB,c= of �' =a --F
<br />b `+ 1+.22
<br />_
<br />s. 34/3'
<br />A, B, b
<br />sin A = a . cos B, b = `/ (c -{-a) (c—a) = c 1— o'
<br />A, a
<br />B, b, c
<br />B = 90°—A, b = 2 cot A, c = 2
<br />sin A.
<br />F
<br />-
<br />A, b
<br />B, a, c
<br />B =90'—A, a = b tan A, e = b
<br />cos A.
<br />o
<br />A, e-
<br />B, a, b
<br />B =90'—.A, a = c sin A, b = e cos A,
<br />r
<br />a
<br />Solution of Oblique Triangles
<br />�. r..�i
<br />Given
<br />A, B, a'
<br />Required
<br />b, c' C
<br />_ asinB asin C
<br />b
<br />' C = 180°—('�L-+ B). c =
<br />sin A sin A ..
<br />i ' m'`` 3�: f�.
<br />_
<br />A, a, b
<br />B, c, C
<br />b sin A cc sin C
<br />sin B = C = 1fi0°—(A i- B), c =
<br />,.
<br />a , sin A
<br />a, b, C.,
<br />A, B, c
<br />A-f B=180°=C, tani(fr~B)=((r-b)tan (!l+B)
<br />a + b
<br />C
<br />Sim A
<br />a, b, c
<br />A, B, C
<br />a+b+c
<br />s= sin''-,A=
<br />2 8 c
<br />sinkf1="')"8c) C=180°—(A+B)
<br />.
<br />..
<br />o
<br />a, b, c
<br />Area
<br />a+b+c
<br />s= 2 ,arca = y s(a—a s—b) (•,—c)
<br />- y
<br />A, b- e.
<br />-Ar . ea
<br />area = b c sin A
<br />2
<br />a2 sin B sin C /+
<br />.
<br />A, B,,C, a
<br />Area
<br />area--
<br />2 sin A
<br />} REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />St¢ooe
<br />cosine of the vertical angle. Thus: slope distance =319.4 fL
<br />Vert. angle=5° IOC Froin "Table. Page IX. cos 61101=
<br />e
<br />c+ 9959. Horizontal distancs,319.4X.9959=315.09 ft.
<br />So �9t
<br />distance timest(lccosi c' f ertcalA,nvie).1Withltnus he
<br />same figures as in the prex:eding example, the follow-
<br />Horizontal distance inresult is obtained. Cosine 5°10'=.9959.1—.9959=.0041.
<br />310.4X.0041=1.31. 319.4-1.1'c1=318.09 ft.
<br />When the rise is known, the horizontal distance is aFiproximately:—the slope dist-
<br />'
<br />- ance.less the square of the rise divided by twice the slope distance. Thus: rise=14 ft.,
<br />slope distance=3026 ft. ' Horizontal distance=302.6— 14 X 1414 =3016-0.32=302.28 ft.
<br />--•
<br />2 X 3)2.6
<br />�.i
<br />MADE IN UA,
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