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I
<br />I
<br />TRIGONOMETRIC FORMULiE
<br />3. B B
<br />V_
<br />a a a
<br />X.
<br />'0000,�
<br />A A
<br />b C b
<br />7.
<br />-Right -Triangle
<br />Oblique Triangles
<br />Solution of Right, Triangles
<br />For An le A" ;- a- b - =
<br />a
<br />4/-
<br />7-03
<br />a
<br />7 an cotsec
<br />c , Cos a cosec
<br />Given
<br />a; b
<br />Required
<br />AB,c
<br />,
<br />tan A = b. cot B,c =. /a-2 +T2 = aT a2
<br />a�,
<br />A, B, b
<br />a2
<br />1-7;_
<br />�4-
<br />A, a.
<br />B, b, C
<br />B=90°—A, b a cotA, a a
<br />sin A.
<br />A, b
<br />B, a, c
<br />B=90*—A,a btan A,C— b
<br />cos A.
<br />b I
<br />B = 901—A, a = c sin,A, b = c cos A,
<br />Solution of Oblique Triangles
<br />9'3
<br />Required
<br />asin B asin C
<br />b= —A
<br />AGiven'
<br />, B,.a
<br />b, c, C
<br />, C 180'—(A + B),
<br />sin sin A
<br />A, a, b
<br />B, 61' C
<br />b sin A a sin C
<br />sin B= a I C = 180'—(A + B), I; = sing
<br />a, b, C
<br />-A, B c
<br />A+B=180*— C, tan J (A—B)=. (a—b) tan �' (A+B)
<br />a + b
<br />a sin C
<br />sin A
<br />b, 6
<br />A, B,C
<br />b
<br />8=,a+.+ I'inlA=I
<br />sin 1B=.)1(s—aT(s—)
<br />ac , C= 180'--(A+B)
<br />a, b, o
<br />Area
<br />a+b+
<br />8 = 2 , area = N1s(s—aY(8—T) (s—e
<br />A, b, c
<br />Area
<br />area = b e sin A
<br />2
<br />A,B,Ca
<br />Area
<br />area a' sin B sin 49
<br />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 />a�starcc
<br />Vert. angle = 50 101. From Table, Page IX cos 50 10f
<br />swlp
<br />.9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />Horizontal distance also= Slope distance minus slope
<br />Pngw
<br />'4 distance times (1—cosine of vertical angle). With the
<br />same figures as in the preceding example, the follow-
<br />Horizontal distance
<br />ing result is obtained. Cosine 5'101=.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
<br />rise divided by twice the slope distance. Thus: rise=14 ft.,
<br />slope Aistance=302.6
<br />ft.
<br />Horizontal distance=302.6— 14 X 14 =302.6—O.32=302.28 ft,
<br />2 X 302.6
<br />MADE IN U. S. A.
<br />a
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