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y. TRIGONOMETRIC FORMUL
<br /> � IE
<br /> •-s B B
<br /> a c a c, J a
<br /> J- b C A� b C A b C
<br /> Right Triangle Oblique Triangles
<br /> l� Solution of Right Triangles
<br /> For Angle A. sin = ,cos= ,tan= b ,cot_.a,sec=b, cosec ,
<br /> ' y Oiven Re4uired a _
<br /> a, b A, B,c tan A= b= cot B,c = a$ a V,+ a$
<br /> 7 G
<br /> 0 3 3 a, c A, B, b �sinA=a=eosAb (c+a (&--a =a 1-2
<br /> /P f. .7 a -- Z a
<br /> -- (� A,a B, b, c B=90°—A.b =a cotA,c= sin A.
<br /> Cl b
<br /> A b B,a, c B=90°—A,a = b tan A,c= C04A. ,
<br /> v <'' `{ / • U A c B,a, b B=W—A,a=a sin A,b=c cos A,
<br /> 6 r Solution of Obiique Triangles z
<br /> j,�-F Given Req'-red a sin B a sin C
<br /> A, B,a b, c, C' b= sinA ' C= 180°—(A+B).a = sin
<br /> — b sin A a sin C
<br /> 7
<br /> A, a, b B, c, C sin B= a ,C= 180°—(A+B),c = sin d
<br /> (a—b)tan (A+B)
<br /> r -- • � ,, d v� ,� I a, b, C A, B, c A+B=180°—C,tans(A—B)= a+. b
<br /> a sin C
<br /> sin A
<br /> a+b+c
<br /> B, C a= 2 ,sin 3A
<br /> Jy _I
<br /> .� cl
<br /> 17S .` sin'B=V(a a c ,C=180°—(A+B)
<br /> . ----
<br /> T G.9l� A a+.b+a
<br /> S� b c Area 8= , area
<br /> bcsin A
<br /> ' , i
<br /> A
<br /> ,. b, c Area area = 2 �b
<br /> az sin Bsin C -
<br /> ' A,B,C,a Area area = 2 sin A
<br /> 3 r REDUCTION TO HORIZONTAL
<br /> 3' Horizontal distanoe=Slope distance rt4ultiplicd by the.
<br /> cosine of the vertical angle us alopedistance=319.4ft
<br /> Vert angle °30'. From able,Page IX.cos b°IW=
<br /> ?'f e aceta �, 98g� p�distance=319 4X'1669=11809fL
<br /> �r also=Slone 0istan6e minus slop
<br /> 3 L? '✓ J 0 "� $�°� po��e o4 eta° � --seine of verdeol angle). With 01b
<br /> res as itt`the preaedg example.the#oubw-
<br /> �'
<br /> i'V` S 0 { N. �. Ing result is py�tsined: 1.31=, 51R,�=.eY68 i-9169=•0041.
<br /> - Horizontal distance 319 4X. ylt1.81A•4-131 gt&o9 ft
<br /> di rrh�oee is approzimately. $e slol�4
<br /> When the rise is of the ,the 4 D the sbsoe distance. lett,
<br /> S - once less the square of the rEaed � �X 14 X281
<br /> 1 ,', v 4 14
<br /> slope distance-30M ft. Horizen -� # 2X302 s
<br /> MADE INU.S.A.
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