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8II
<br />Nature
<br />TRIGONOMETRIC FORMULWE 3 L 37n/-
<br />2
<br />AnMe, Sin, Tan. 9as� Caua. 1- Z z 3 I G. S B B
<br />02 1.17921.8871, l yi i'� y f1 Z t f [t c 1 l' c a i �: .
<br />1 .5324 .828 1.13131.37 � 7" , � A
<br />.b3 .83 .i 2
<br />1.1 _ Y,'rya u4 /Z�, G C �b C i.
<br />3 .5373 .8371 __;4, , �"'—� o d
<br />5393 �' 0 3 6 �� Right Trian le C
<br />A
<br />G i
<br />g Oblique Triangles
<br />Solution of Right Triangles i 7 6 i
<br />�; t �`'�= n ; .�. For Angle A. sin = a cos = b ,tan = as b e i t 99
<br />l , 9 1 J d Q - !j • {� (, ;4 Given I Required c r a b .cot = 2 ,sec = b . cosec = C
<br />7 a, b A; B c a
<br />G tan A=b=cotB,c= a�+ z=a 1+ z
<br />d- i a
<br />r 4'I / /Q ? l o, c . \ 6 �_ ° A, B, b sin A = = cos B, b = .,/ c f u) (c—a) = c
<br />-- _ 3.717,0V1—
<br />/0'.72- a1� A b, ° B=90°—Ab=acotA,c= a VV u2
<br />,� LC
<br />r1 Z 5 '6 sin A.
<br />' Ii..' J'Z 9 t , b l B, a, c B=901—A, a = b tan A, c= b
<br />s a --z r t ` cos A!+`s
<br />y 7 / �,T $ ' 'r e 9 3 - 7 L t 9. may` A' ° B� a> b B = 90°=A, a = c sin A, b = c cos A, L• 2 0
<br />/ 7 7�, f 1 ` '% 3_ f-ye Solution of � Oblique Triangles s �
<br />1 f moven' Required F
<br />L3 �r 3" _ pl_/ .s,`� Bs a- b, c, C I b=annA ,C=180°—(A+B)�c=a C
<br />.>-a0 ��. sin A
<br />7 �� 3�' bsinrl
<br />17r J , a, b B, q C sin B= ,C= 180'—(A asin C
<br />�.#. 3'3.3 X 1.6 sin A )
<br />- ,49
<br />4F & 1 7 Z�-�'} \ �, y A, B, c 04&-B-1800— C, tan-', (A—B)- a—b) tan (A-} B) 2
<br />d c7�? Zs �iJ c=asinC a + b
<br />i l.. 3.r.
<br />_ 0. " (� I h� - _,..,,.,s� 7 9 2p sin A "3 i b
<br />Y, t 3 b �3: 2
<br />A, B; C
<br />731" Z8.rr ".� 1 be i,.2 k.r i
<br />sin 2B=-/a)(s—e ,sy ,y
<br />V a c i 180°—{A� B)
<br />� ?2 0
<br />a� b, c Area a = , area /,.1-
<br />A, b, c Area area = b c sin A 3 f
<br />3 ' 7 f 3 y 3`al l ,� "y l A, a Area C
<br />B, , area = a2 sin�n C
<br />3 S` 2sinA
<br />REDUCTION TO HORIZONTAL -,-yam
<br />Horizontal distance=
<br />7 cosine of the vertical a; e� dist °Pe multiplied by the
<br />oe
<br />I m �' Ho#el� b° 10,. From Table. Pads IX oos 60 11Y=
<br />1/ X04 e a ntsl distance-819.4X.VM-31&00 ft.
<br />y i 1+ fx ilorizontai distance also distance
<br />j j a �t distance times (1-cosine of vvertical angle ppee
<br />WAS i the
<br />�' ( o same figures as in the rec exampl% the follow-
<br />--
<br />rizoatai dista>toe ing result is obtained. Cosine b 30,=.9Wij.,lige
<br />319.4X.0041=1.31.319.4-131=31&o91'
<br />iVhea the *"Aft Of Offttherrise divithe ded distance is aDDreziasaet .-the dope dist-
<br />leas tLe
<br />-- Y lance the slope distance, Thus: rise=14 ft.,
<br />: rw De.ftMuwe-3otl.8ft. HorUoatsl. � 1
<br />„ . ce=3o2Q -
<br />30228 2XM
<br />48-p,32=R
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