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<br />TRIGONOMETRIC TORMUL&
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<br />/J__a c a e
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<br />Right Triangle L Oblique Triangles
<br />10._ Solution of Right Triangles
<br />!fid , �� 5 For Angle A, sin = , coo= , tan = b , cat = a , see = cosec = a
<br />Giv'en
<br />Required ,y a
<br />a b B,. B ,e tan = b =col B, c • a + ' = a 1 f ax
<br />f,fa� Uc47 s7
<br />(�f Z
<br />• J -� 3• a, a A, B, b sin A = ! = Cos B, b - \/(c+ii (e—a)
<br />t
<br />A,a B,.b, a B=90°—A;b=acotA,c
<br />-" sia A.
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<br />8 f _ A, b B, a,. e B = 90'—A, as = b tan A, c = cos
<br />A, c B;. a, b B= 90°—A, a = coin A.
<br />5= I.. A,
<br />Solution of Oblique, Triangles_
<br />Given Required ay sin B 'z "in C
<br />� r; A i3 a b; c, C b= ,C=1'80°--(A+B)�a=
<br />sin A sin .A.
<br />11
<br />Aa sin C
<br />-173'-173' a, b B, c, C sinIV g= a ,= 180'—(A -t-.B)., c = _•sin A
<br />r�LL - a, b, C d; B, e A+B-180°— C, ten.7�(A—B)i(a")) +
<br />f/ F a sn C
<br />$ + / — 3J a' b' c A, B, C s—,sinJA—
<br />�jis_ b(e
<br />vvv
<br />�! ✓� r ) 4 sin 0B— (sia a ), C=180°—(A+B)
<br />a+b o
<br />a, b, c Area s — 2 area= NIs (s —a s— ) (s—c)
<br />1 r , f ` -` `l A, b, c Area area = b e s2 A
<br />r+
<br />Cr
<br />I A, B, C, a Area area = 6l Bim B Bin 2 sin A
<br />� REDUCTION TO HORIZONTAL
<br />_ Horizontal distance= Slope distance multiplied by the
<br />e
<br />cosine ofthe vertical angle. Thus: slope distance =919.4 ft.
<br />nc a Vert. angle
<br />a 51 l distan m ale, Page IX. cos 51 id=
<br />( c 4X.9959 918.09 ft.
<br />F �� [, 51Ope eagle Horizontal distance also= Slope distance minus slope
<br />distance times (1 --cosine of vertical angle). With the
<br />y I 4e same figures as in the preceding example, the follow -
<br />C3 / Horizontal distance ft7 ingresult is obtained. Cosine 5°10'=.9959.1—.9959=.0041. �• 319.4X.0041=1.31. 319.4--].31=318,09 ft.
<br />�' _ _ 0'i7 "' , 9 e' -• _ When the -rise is known, the horizontal distance is approximately:—the, slope dist-
<br />ri
<br />ante less the square of the rise divided by twice the slope distance. Thus: se=14 ft,
<br />slope dis1ance=30281L Horizontal distance=SMtS72 4 1 0=BM! x.32 =30225 ft ,
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