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12, 5 --
<br />--- / — S
<br />,3 - 5K
<br />,,�s
<br />T
<br />{
<br />Qi
<br />a sin A
<br />3�
<br />00 ,
<br />TRIGONOMETRIC FORMUL&
<br />B B B
<br />a c a o a
<br />A. b C, Ab C, A b
<br />�—1 c
<br />Rigbt'Triangle Oblique Triangles
<br />Solution of Right Triangles
<br />a b - a- - b c c
<br />For Angle A•` sin = , cos = , tan= b , cot = a —,see = b , cosec = a
<br />Given Required a2
<br />a,b A,B,c tanA=b=cotB,c= as { b2=a 1+
<br />as
<br />a
<br />• a, c A, B, b sin .A = a = cos B, b = \/ (c-{- a) (c—a) = c 1— a
<br />A, a B, b, c B=90°—A, b= a cotA, c= a
<br />sin A.
<br />A, b B, a, c B = 90°—A, a = b tan A, c = b
<br />cos A.
<br />A, o B, a, b B = 90°—A, a = e sin A, b= c cos A,
<br />Solution of Oblique Triangles
<br />Given Required a sin Ba sin C
<br />A, B, a b, c, C b ' C = 180°—(A } B), c =
<br />A sin A
<br />{
<br />b sin A a sin C
<br />A, d, b B, c, C sin B = , C = 180°—(A { B}, c =
<br />a sin A
<br />a, b, C A, B, c A+B=180°— C, tan I (A—B)= (a b) tan z (A+B)�
<br />a + b
<br />a sin C
<br />_
<br />c sin A
<br />a+b+c
<br />b, c A, B, C s= 2 sin'A= Al b e '
<br />sin ac
<br />ac ,C=180°—(A+B)
<br />a, b, c Area s=a+_2+c, area = s(s—a)(s—b)(s—c
<br />I
<br />0
<br />bcsin A
<br />A, b, c Area area =
<br />2'
<br />as 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 />i
<br />cosine of the vertical angle. Thus: slope distance=319.4ft.
<br />taoce Vert. angle =5° 10. From Table, Page ix. cos 51 ld=
<br />aye H 9959. Horizontal distance=319.4X.9959=318.09 ft.
<br />'� oQe distance
<br />1Withlthe
<br />An��e distance (1—cosine oflvertical angle).tance
<br />timest(1
<br />Qe
<br />same figures as in the preceding example, the follow -
<br />Horizontal distance ing result is obtained. Cosine 50 101=.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 />anee less the square of the rise divided by twice the slope distance. Thus: rise =14 ft.,
<br />slope distance=302.6 ft. Horizontal distance=302.6— 14 X 14 =302.6-0.32=302.28 ft.
<br />2 X 3026
<br />MADE IN U. S. A.
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