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e a o r L 7 —j-J..— 7 TRIGONOMETRIC FORMUEfE
<br /> I 99 �b lv. B B
<br /> A
<br /> o b C /G q
<br /> A A d"
<br /> a C 1 �
<br /> h
<br /> Rigt Triangle
<br /> Oblique Triangles o $ "
<br /> 8 r `7s Solution of Right Triangles 0
<br /> !•f =For Angle A. sin = c ,cos= ,tan--fib—,cot= b—,see =a, cosec=,.ell
<br /> a�y 3
<br /> ( f j t C1 / 8�O. ��S (liven Required a a $ a
<br /> 4
<br /> a, b A, B;c tanA= b= cotB,c = a + s= a 1 � z
<br /> %t . p I i {'y{ az
<br /> a, a A,B, b sin A=a=cos B,b=%/Ta—+a—)T6--) =a I a2
<br /> 4
<br /> b
<br /> "L A, B, b, c B=90°—A,b =acotA,c= a — —
<br /> sin bA. _
<br /> �.
<br /> A, b B,a, e B=90°—A,a = b tan A,c= cos A.
<br /> -3
<br /> c $
<br /> f7 l A,o B,a, b I B=90°—A,a=a sin A,b= c cos A, yob
<br /> b 3 1 , Solution of Oblique Triangles
<br /> (liven Required a sin B a s n C
<br /> ?j y " _ __ -. A, B,a b, c, C b= sin - , C= 180°—(A+B), c =
<br /> sin A
<br /> 7^ �f_l A, a, b B,c, C sinB= b a A,C= 180°—(A { B),a = E!!2-9�G�'i^
<br /> sin A
<br /> •J y
<br /> 1"i, ;t �jj `i' ► ay b, C A, B,a A+B O°—C,tan z(A—B)= a—b)tan a_(A+B)
<br /> M�'� c = asinC ?+' r1C.d i.
<br /> y, '7o \ -.� sin A 4.87
<br /> Q
<br /> --�
<br /> 1,2'11 •fir� ! 4t
<br /> � a, , a A C s=Q�+h+c 2 ,s ,A l8- bs
<br /> �Y V' J AL 1 y tC le' ti 5:7`x, (� ing =J e er` f✓ !S
<br /> �cTL%n'BI s
<br /> ac �C=180°—(A+B)? G 9
<br /> z V
<br /> D
<br /> a b
<br /> a, b, a ren s= +2+c, area = s(s—a s— (s—c 7,
<br /> S A, b, c Area area = b e sin A L ^s. a •3 7.4r�
<br /> -- y az sin B sin C i
<br /> S l 3 A,$C,a Area area = 2 sin A /� I
<br /> y ,,, 1 3 J— REDUCTION TO HORIZONTAL
<br /> 8 7 4— Horizontal distance=Slope distance multiplied by the
<br /> 7 3 z4 C) cosineofthe vertical angle.Thus:slope distance=319.4 ft.
<br /> Vert. angle=50 101. From Table,Page IX.cos 50 301=
<br /> Horizontal
<br /> �. o0e w 9959. distance=319.4X.9959=31&09 ft.
<br /> f d - �►. ! ' 6� Arg1e Horizontal distance also=Slopedistanee minus slope
<br /> • (0 y A , distance times Ei—cosine ofv Ileal angle). With the
<br /> J same figures as in the preced�ei�example,the follow-
<br /> Horizontal distance ing result is obtained.Cosine 51101—.9959.j—.9m=.004L
<br /> - ✓_ q 319:4X-0041=1.31.319.4-1.31=318.09 ft.
<br /> p When the rise is known,the Jwrizontkl distance is apswkimatelyc—theslope dist-
<br /> ance less the square ofthe rise derided by tw,,the slope distance. Th
<br /> qs:rise=l4 ft.,
<br /> S I slope distant 3028 ft PlorizonW distasee�g.._14 X14_=".=
<br /> u 2,X=16
<br /> MADE IN U.S.A.
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