(a) Without using Mathematical tables or calculators, simplify : \(\frac{2\tan 60° + \cos 30°}{\sin 60°}\) (b) From an aeroplane in the air and at a horizon...

(a) Without using Mathematical tables or calculators, simplify : \(\frac{2\tan 60° + \cos 30°}{\sin 60°}\)

(b) From an aeroplane in the air and at a horizontal distance of 1050m, the angles of depression of the top and base of a control tower at an instance are 36° and 41° respectively. Calculate, correct to the nearest meter, the :

(i) height of the control tower ; (ii) shortest distance between the aeroplane and the base of the control tower.