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,-TRIGONOMETRIC F li r
<br />,� _C ORMUL�E'
<br />B �P B
<br />{
<br />ZT ��# t,
<br />b yRtgtTriangle Ohlli9ue Triangles
<br />b -- Solution of Right ITrianglesr- rt ' ✓�
<br />a b a.
<br />For Angle A. `sin' _ - , cos = - tan= , cot=—
<br />c:sec = ,cose
<br />Given Required
<br />G j % c ' S a b
<br />. a a
<br />a, + b
<br />a, c. A, 33, b }a}lc-a)
<br />A., a B, b, c. .B=90* --A, b=.acclt_A,c= a
<br />sin A. i1
<br />��.� ° ��A,b' B,a,c B=90°-A,a=Lta.cA,c= b edZ_
<br />coo. A. -
<br />�'+- _ A, c F3, a, h B =90'-A, a = c siva A, b = e cos A,
<br />Solution of Olalique 'Triangles'
<br />ori G U Q ` D mss' *r Given . Required ? .
<br />a sin B 'Bin C 1 r
<br />A, 17 `a b c, C b = C = 1BU =(A -F 'B) C = -
<br />� . ✓' '. f l j '' sin tl sin A '
<br />h sin A
<br />sin
<br />A, a, b' •1V, e, C. sin Ii = a C = .l f B), c = (sin A
<br />r.
<br />a -b) tan z (A+B)
<br />a•, A+B=180'-G!,
<br />a + b
<br />a sin C ;
<br />sin A Vis`
<br />U �•% - l a, b, c A, B,.0,-
<br />' b c '
<br />(S sin B3 141 a c c'C=180'-(A. { B) 4�
<br />a, b; c Area s= 2 area = s(3 -a) (s -b) (s --c)
<br />A, b a Area area _ b c sin. -A r ��
<br />t 2
<br />J
<br />_ a' Sln - •.
<br />A. B, C, Area area - B"sin C J
<br />2sin d
<br />REDUCTION TO HORIZONTAL
<br />Horizontal distance =Slope distance multiplied by the
<br />e cosine oithe vertical.:angle°Thus: slopedistanee=310.4ft.
<br />aLSta.T,e Vert. angle=P 1p'. From Table, Page IX. cos 50 l0'=
<br />9959. Horizontal distance =319.4X.9959=318.09 ft.
<br />Horizontal distance also=Slope distance minus slope
<br />. - e ti distance times (L—o*sine of 'vertical anele). With the
<br />z V same figures as in the preceding example, the follow -
<br />horizontal distance
<br />ing result is ottainerd. Cosine 51 10'=.9959. 1—.9959=.0041.
<br />• � a 319.4X.6041=1.31. S19.d-1.3i=319.69 ft.
<br />(� When the rise is ]mown, the horizontal distance is approximately:—the slope dist-
<br />( ante less the square of the rise. divided by twice the slope distance. Thus: rise —14 ft..
<br />U slope distance=302.6 ft. Horizontal distance=3(L6-- 14 X 14 =302.".B2 30228 ft.
<br />a
<br />2X302.6
<br />MAGE IN V. B. A.
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