(a) Using a ruler and a pair of compasses only, construct a parallelogram PQRS with diagonals |PR| = 9cm and |QS| = 6cm, intersecting at K and < QKR = 60°.
(b) Construct a rectangle PABS which is equal in area to PQRS in (a) above and on the same side of PS as PQRS. Measure |PA|.
From a horizontal distance of 8.5 km, a pilot observes that the angles of depression of the top and the base of a control tower are 30° and 33° respectively. Calculate, correct to three significant figures :
(a) the shortest distance between the pilot and the base of the control tower;
(b) the height of the control tower.
