a). In the diagram, AOB is a straight line, <AOC  =  3(x  +  Y)°,
                 <COB  =  45°, <AOD  =  (5x + y)° and <DOB  =  y°.  Find the

                   values of x and y.

b). From two points on opposite sides of a pole 33 m high, the angles of elevation of the top of the pole are 53° and 67°.  If the two points and the base of the pole are on the same horizontal level, calculate, correct to three significant figures, the distance between the two points.

observation

This question on the angles at a point did not pose any problem to majority of the candidates 3(x + y) + 45  =  180° >>  3x  +  3y  =  135  =  x + y  =  45 ………..  (i)
5x  +  2y  =  180  …  (ii).  Putting  (i)  into  (ii)  gives
5x  +  2(45 – x)  =  180 >>  3x  +  90  =  180.  Hence  x  =  30 and from (i),  y  =  15.

The (b) part was not well handled.  Many of the candidates could not draw the correct diagram.
XZ  =  XP  +  PZ  =       33     +      33       =   38.9 m  to  3 sf.
                              tan53°       tan67°