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<br /> ?/ J TRIGONOMETRIC FORMULAE
<br /> B B B
<br /> la c a o a
<br /> �yr� A
<br /> b C b CA b L'
<br /> Right Triangle Oblique Triangles
<br /> Solution of Right Triangles �--�
<br /> a b a b c o
<br /> For Angle A. sin = ,cos= ,tsa b,cot = a,sec= b, cosec= —
<br /> f j Given Required a
<br /> $ a
<br /> Q� �3�� �" a, b A, B,c tan A= b= cot B,c = a + x = a 1a
<br /> gyp(; f j + a
<br /> a, c .A,B, b sin A= =cos B,b= e a a
<br /> A,a B, b, a B=90°—A, b =acot A,c=
<br /> sin A.
<br /> �5 n
<br /> A, b B, a, a ,B=90°�A,a = b tan A,c= cos A.
<br /> J r �.
<br /> c
<br /> �! � A, c B, a, b B=900 A,a—o sin A,b=c cos A, "
<br /> 1 v(6L .� `„r Solution of Oblique Triangles, Given Required a sin B
<br /> b = ,A, B,a b, c, C C= 180°—(A+B), c = s A
<br /> sin A
<br /> bsinA
<br /> j a sin C
<br /> �, ,�✓:,�/Cg; A, a, b ' B, o, C ein B= .�'= 180°—(A t B),c =
<br /> sin A
<br /> (a—b)tan s( +B
<br /> S i
<br /> a, b, C A, B, c A+B-180°—C,tan 2(A—B)= �_ A B
<br /> a sin C a b
<br /> sin A
<br /> ° 3
<br /> b, o A, B, C a=a+2 ,sin;A=��s b
<br /> moi- .:.., _.x , sin IB= I(x—axa—c ,C-180°--(A+B)
<br /> 1I a c
<br /> q b, c Area 8=a+Z+c, area = s(a—a s— s—e
<br /> A, b, c Area area — b c sic A
<br /> / x % —
<br /> f
<br /> A B C s Area area =a'sin B sin C
<br /> L' 2 sin A
<br /> Q,1 �: � l C� � -
<br /> c REDUCTION TO HORIZONTAL
<br /> Horizontal_f---� J; j .;
<br /> / ' � cosiaeofthe erticalan¢Ie tance Thudistance
<br /> slope distancemultiplied
<br /> p"e 9 4fL
<br /> C --G—
<br /> � '
<br /> Vert. angle=6°10'. From Table,Page IX cos 6°1th
<br /> w=
<br /> 3 j oPe a 9869 Horizontal distance. 519 4X.9869=518.09 ff
<br /> Ale horizontal distance also—Slope distance minus slope
<br /> } rr distance times(1—cosine of vertical angle). With the
<br /> b $prjTgnwnce isame
<br /> g eslalat is obtainedCosinepreceding
<br /> b°a10�=aagmple,the follow-
<br /> 1
<br /> �y * 819.4X.0041=1.51.919.4-1.01=51&09 ft.
<br /> When the rise Is known,the horizontal distance is approximately:—the slope d�
<br /> -leas the square of the rise divided by twice the slope distance. Thus:rise=l4 St,
<br /> slope distance-30U ft. 8rrlaafal 4101211ee—Mi..•14 x 14.•r�26-g,$�80 MUM
<br /> $X565,6
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