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30
<br />�7
<br />8 �9-
<br />a
<br />8 x,40
<br />M
<br />�TRIGOI'VOMETRIC FORMULIE p
<br />B B:
<br />a c a c
<br />a
<br />2
<br />�b C A�b C A b C
<br />Right Trianile Oblique Triangles J
<br />`';Solution of Right Triangles
<br />For• Angle A. sing= o ,cos = b. ,tan = b ,cot = a sec = b ; cosec= a
<br />Given Required a 2
<br />a,b A, B,6' tan A=b=cotB,c= a2=a l+as
<br />a, a A, B, b� sin A = C = cos B, b = \/ (c+a) (c—a) = c 1— a,
<br />A, a B, b, c B=90°—A, b= acotA, c= a Y
<br />sin A.
<br />A, b
<br />B, a, c
<br />B = 90°—A, a = b tan A, c — b
<br />COs A.
<br />A, c
<br />B, a,. b
<br />B = 90°—A, a = c sin A, b = c. cos A,
<br />Solution of Oblique Triangles
<br />Given-
<br />Required
<br />A, B, a
<br />b, c, .0
<br />b , C = 180°—(A + B), c =
<br />sin -A sin A
<br />A, a, V
<br />B, c; C
<br />b sin Aa sin C
<br />sin B = , 6 = 180°—(A + B) , c —
<br />a sin A
<br />a, b, C
<br />A, B, c
<br />(A—B)= (a—b) tan z +B)
<br />A+B=180°— C; tan 1.a
<br />-}- b
<br />b
<br />a sin C
<br />c=
<br />sin A
<br />a, b, c
<br />A B, C
<br />s=a+2+c,,in!A=��s— b(C
<br />sin?B= (8—)(S—),a C=180°—(A+B)
<br />a, b, a,
<br />Area
<br />8=a+2+c, area =s(s—a (s— ) (s—c
<br />A, b, c
<br />Areab
<br />C sin A
<br />area =
<br />2'
<br />aQ sin B sin C
<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 />cosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />a�stQoce
<br />Page JX. Cos b° 101=
<br />e
<br />'Ie
<br />y99 9. Horizontal distance 319 4X.995 3 8.09 ft
<br />glop
<br />a Horizontal distance also=Slone distance minus slope
<br />Ve
<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° 101=.9959.l--9959=-0041-
<br />01=.9959.1—.9959=.0041.319.4X.0041=1.31.319.4-1.31=318.09
<br />319.4X.0041=1.31.319.4-1.31=318.09ft.
<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.
<br />Horizontal distance=3026— 14 X 14 =302.6—O.'32=302.28 ft.
<br />2X3026
<br />WOE IM U. 6. A.
<br />u
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