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G .moi 7
<br /> 3. "TRIGONOMETRIC FORMUIaE
<br /> a c :a a
<br /> -- A
<br /> o �,,.� �> k" d y d
<br /> C b /
<br /> ' 3• Y __ ? Rigfit Triangle Oblique Triangles
<br /> '_T 3 y y � Solution of Right Triangles
<br /> a b a b c
<br /> l
<br /> 76 ,
<br /> For Angie sin= ,cos= a ,tan= b ,cot= ,sec= b, cosec=
<br /> L• d' Given Required
<br /> b A, B,o tan A=b= cot B,c= al+ s =a 1
<br /> Z,.5'
<br /> z y 3 y 8 a, o A,B, b sin A=a=cos B,b -02,
<br /> a
<br /> v— — d>a B> b> o B=90°—A,b=a cotA,a= sin d,
<br /> b B,a, o B=90°—d,a= b tan A,a=_b
<br /> A.
<br /> A,a B,a, b B-90°—d,a=a sin A;b—a cos A,
<br /> Solution of Oblique Triangles
<br /> Given Required Solution
<br /> Gin B
<br /> t 4�• T d, B.a b, o, Cb- sin d ' C= 180°—(A+B),o sin
<br /> d
<br /> y y 2 j p a f' d, a, b B,a, C sin B= b sin A C= 180°—(A { B),a= sin A a sin C
<br /> S> . O
<br /> .2 9 f "rq 7 S^ S— �+ a> a A,B,o A+B=180°—0,tan j(A--B)--(")tan j(d+B)
<br /> a+b
<br /> = '
<br /> a sin C
<br /> 1 r= �/
<br /> a �
<br /> 7 S y ti l �y L 0 � S� / �.�..sin A
<br /> i 3_
<br /> S._ — iA—S `i b, a d, , C ea—�b ,mnla_ 8_d
<br /> - — bo
<br /> 2 —
<br /> ac C=180°--(A+B)
<br /> r G �' .. s, b,.o Area s �, area
<br /> 3 j GJ d, b, e Area area = bei A
<br /> ��
<br /> ''_' 3 f, a'do B sin C
<br /> A,B,C,a Area area =
<br /> 4c/ 2 sin A
<br /> REDUCTION 3 L v RUON TO HORIZONTAL
<br /> y. 3 Horizontal distance=Stave distance multiplied by the
<br /> cosine of the vertical angle.Thus:slope 919 4 ft
<br /> 4 t* Vert a6°1Q'. From wits,Page cos b°lo>=
<br /> distsaco
<br /> 8868 Horizontal distaacm=91S.4XAM19-1lSt�s�oe n,
<br /> Horizontal distance also=Slope distsaleh•min]�8 Slav
<br /> 3 distance times(1—cosine of vertical an¢te).With tLe
<br /> �s ggases as in the preceding ezunple,the 1pllow-
<br /> 0 izontal dWan" 4IS btai sine
<br /> 50 t..8860.y-.9B8B�.U041,
<br /> v , When the rise is k'own,se tlLtance is ss►prozimatel the slope dist-
<br /> slope
<br /> less the square of the rise bYtzrice the slaps distance Thus:rise=l4 ft.,
<br /> slope'iistaace= 028>t fIorttpnt$dlsty J ,s X92=902.28 it.
<br /> "+� MADE M U.&A. H-
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