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TRIGONOMETRIC FORMUL S
<br />N B .
<br />e'
<br />a c a c a.
<br />A�b C A G
<br />Right Triangle Oblique Triangiea
<br />"'Solution of Right .Triangles
<br />li For Angle A, - sin = cos = b —,Ian= a b c
<br />E , e , b ,cot = Q ,sec = b, cosec = a
<br />Qiven _ Required
<br />a,o tan A'=a—b= cot B,c- a7+ 7=a I az
<br />a, c A., B, b sin A = = cos B, b = �/ o+a (tea) = c 1— 03
<br />4, a
<br />B, b, a
<br />B= 90`—A, b= a cot -A, o= a
<br />sin A,
<br />A, b -
<br />B, a, c
<br />B = 90'--:A,4 = b tan A,. = L
<br />cos A.
<br />A,,a
<br />B, a, b
<br />B=90°—A,a=-e sin A,b=6co6A,
<br />i k
<br />Solution of Oblique Triangles
<br />(llveu-
<br />A, B, a
<br />Required
<br />c, C
<br />b = a sin -B
<br />, C = + B), c =
<br />,b,
<br />180°=(A
<br />sin A
<br />('
<br />A, a,. b.
<br />B, e, C
<br />b sin A a sin C
<br />sin B= ,C= 180°—(A +B),,—
<br />a ' sin A
<br />a, b, 0.
<br />A, B, c
<br />A-}-B--180°—C, tan +}(A—B)=(a—b) ten 'z (A { B}
<br />a -I- b
<br />a sin C
<br />4
<br />_
<br />E =
<br />sin A
<br />b, .o
<br />A, B, C
<br />s _ a+b +a
<br />,sin',A=
<br />g. F
<br />E b c
<br />�
<br />ain:}B= ,C-180°—(ASB)
<br />a c
<br />a; b, E
<br />Area
<br />s = 2
<br />A, b, c
<br />Areaarea
<br />= b -e sin A
<br />2
<br />�,-
<br />ai sin B sin C
<br />A, B, C, a
<br />Area
<br />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 =919.4 ft
<br />a�5taoce
<br />Vert. anile=501(Y.' From Table, Page IX. cos 51 IV=
<br />8959. Horizontal distance=319.4X.9959=318.09 ft
<br />g1o4e
<br />ha�1e,
<br />a Horizontal distance also =Slope distance minus slope
<br />�e
<br />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°!0'=.9959. ]—.9959=.0041.
<br />919.4X.0041=1.31. 318.4-1.31=318.09 fL
<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=l4 ft.,
<br />slope distance=3026 ft.
<br />Horizontal distance=3426— 14 X 14 =3926-0.32=302.38 tL
<br />�
<br />_ 2X902.6
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