ANSWERS. l8l 



(22) r=iVs^; A = c=tVsir; B=W. 



(23) S + 3/?=T, 30</?<6o; 0=6o. 



(24) Resolve the components P lt P% along the bisectors of 0. 



(25) J^tana; 13.4, 35.0, 107.2, 572, oo pounds. 



Pages 56-58. 



(2) R = 6, and acts along 5. 



( 3 ) T=W-a/c, P=W.t>/c. 



(4) A C must bisect the angle BCW. 



(5) R* = A 2 + B* + C 2 + 2 BCcosa + 2 C^ cos/? + 2^ cosy. 



(6) Compare Arts. 90, 92. 



(7) The sum of their moments must vanish for two points in the 

 plane not in line with their point of intersection. 



(10) P=$W; T=^W. 



(i i) T= W; P= 0.89 JFalong the bisector of BCW. 



(12) P= Wsm(a+/3) sin/3 becomes a maximum for )8 = (7r )/2, 

 i.e. when the sail bisects the angle between boat and wind. 



w 



, (14) Tension in ^^ and CD=W'l/ 

 where ^= V/ 2 - i(^- /) 2 . 



(15) The resultant acts along the diameter through A, and is in 

 magnitude equal to the perimeter. 



(16) P(i + V2). 



(17) (a) WsinO, fFcosfl; () W^tan^, W/cosO ; (c) 



(20) Produce BO to the intersection Z> with the circumscribed 

 circle ; then DA is equal and parallel to the resultant of OA, OB. 

 DAO'C is a parallelogram ; hence DA = CO 1 . 



