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TRIGONOMETRIC FORMULfE
<br />B c a4 c B
<br />r
<br />b. CA�b C� b C
<br />Right Triangle Oblique Triangles
<br />Solution of Right Triangles
<br />For Angle A. sin = c a , cos = c b , tan= a , cot = b a , sec = , cosec =
<br />b b
<br />Given Required az
<br />a,b A, B4O tan A=b= cot B,c=N/—a-2+-T2 = a 1-I a2
<br />a, c A, B; b 2
<br />sin A = = cos B, b = �/ (c+a) (c—a) .= c 1— u 2
<br />} A, a B, b, c B=90°—A, b = a cotA, c= sin A.
<br />A, b B, a, c B = 90°—A, a = b tan A, c = b
<br />cos A.
<br />A, c B, a, b I B = 90°—A, a = c sin A, b = c cos A, '
<br />Solution of Oblique Triangles
<br />Given Required
<br />A, B, a b, c, C b = a sin B � C = 180°—(A + B), c = a sin C
<br />sin A sin A
<br />b sin Aa ,in C
<br />A, a, b B, c, C sin B= a ,C = 1800—(A + B), c = sin A
<br />z
<br />a, b, C d, B, c A+B=1800 1(a—b) tan (A+B) — C, tan ; (A—B)= a + b ,
<br />a sin C
<br />c— sin
<br />a+b } c
<br />a, b, c A, B, C s = 2 "in ;A= b c '
<br />sin s B= `I (s— )( , C=180°—(A+B)
<br />a+b+c
<br />a, b, c Area s= 2 - ,area = s(s—a s—) (S—c
<br />A, b, c 'Area area = be sin A
<br />j2 Isl.39_000Qo
<br />1 a2 sin B sin C
<br />A, B, C, a Area area = 2 sin A -----
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance= Slope distance multiplied by the
<br />Stance
<br />cosine of the vertical angle. Thus: slope distance =319.4 ft.
<br />, Vert. angle=5' 101. From Table, Page IX. cos 51 101=
<br />a �+ 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />S,oPe ,%Ae a Horizontal distance also=Slope distance minus slope
<br />Ve �. l' 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 51 101=.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 rise divided by twice the lope distance. Thus: rise=14 ft.,
<br />--
<br />14.X 147
<br />slope distance=302.6 ft. Horizontal distance=302.6 —3026-0.32=302.28 ft.
<br />X 302.6
<br />j 1-1.5 MADE 1a V. &h
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