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TRIGONOMETRIC FORMULX
<br />�( a a a
<br />i L A A - C
<br />b. C b C - G
<br />r"'-� Right Triangle Oblique Triangles
<br />y� 7,vc y 'Solution of Right Triangles
<br />j? a b a- b c c
<br />J. - .For Angle A. sin = c , cos =o , tan= b , cot= a , scc = b , cosec=
<br />a
<br />y. Given Required -)- s ! -- _"_------ ----� a, b A, B ,c tan.A = b = cot B, c = a2 2 = a
<br />' 1 :
<br />c A, B, b sin A = = cos B, b = �/ (c+a (e—a) = c
<br />.II vv
<br />--" A, a B, b, c B=90°— b =a cot. c= a
<br />sin A.
<br />A, b B, a, c B = 90°1 , a = b tan A, c = G
<br />cos A.
<br />A, c B, a, b I B — 90*— A, a = c sin A, b= c cos A,
<br />23 Solution of Oblique Triangles
<br />Given Required
<br />asinB —asC
<br />A, B, a b, e, C b `
<br />sin A ' C = 180*—(A + B), c in
<br />— sin A
<br />0 r y t b sin A ,— asin C
<br />A, a, b B, c, C sinB= a ,C=180 (A+B),c= sin
<br />o , (a—b) tan 1,(A+B)
<br />(' { �' • ,)/ )' _ a, b, C A, B, c A+B=180 — G, tan l}(A—B)=a + b ,
<br />'; t .� asin C
<br />3
<br />- q a+b+c
<br />a, b, c- A, B, C s .sin ,sin IA= b c
<br />8 - . s—a) s—c
<br />I J v + Bin +}B=� a c ,C-180'— (A+B)
<br />i T Y a b+
<br />a, b, e. Area s= 2 , area =s(s—a I, ) (s—c
<br />CIO� -b, c Area b. a sin A
<br />A
<br />, area = 2.
<br />a' sin B sin C
<br />( A, B, C, a Area area =
<br />O 2 sin A
<br />I J 2 1 REDUCTION TO HORIZONTAL
<br />it � � � .. _ : Y``-'•'�`� � Horizontal distance=Slope distance multiplied by the '-
<br />I ` e cosine of the vertical angle. Thus: slope distance=319.4ft.
<br />1 %' �h gt9re Vert. angle=5° 101.' From Table, Page IX. cos 50 W=
<br />J - 3v4' 9969. Horizontal distance=319.4X.9959=318.09 Pt
<br />Horizontal:distarice also= Slope distance minus slope
<br />NNyNN(
<br />�e
<br />lf� r,"1 distance times ,(1—cosine of vertical angle). With the
<br />'.. _ same figures as in the preceding example, the follow-
<br />' I C Horizontal distance ing result Is obtained. Cosine 5°101=.9959.1—.9959=.0041.
<br />919.4X.0041=1.91.919:4-1.91=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 slope distance. Thus: rise=l4 ft,
<br />a. slope distance=3028 ft. Horizontal distance—`3M6 — 14 X 14 2X302.8 028 =8-0.32=90228 &
<br />�� - - •� - �-- .. - .. .
<br />MADE IN U.
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