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.

(a) Simplify \(\frac{0.016 \times 0.084}{0.48}\) [Leave your answer in standard form].

(b) Eight wooden poles are to be used for pillars and the lengths of the poles form an Arithmetic Progression (A.P). If the second pole is 2m and the sixth is 5m, give the lengths of the poles, in order.

Show on a graph, the area which gives the solution set of the inequalities: \(y - 2x \leq 4 ; 3y + x \geq 6 ; y \geq 7x - 9\).

(a) Prove that the sum of the angles in a triangle is 2 right angles.

(b) The side AB of a triangle ABC is produced to a point D. The bisector of ACB cuts AB at E. Prove that < CAE + < CBD = 2 < CEB.

A carpenter was told to make a rectangular desk with top of dimension 50cm by 40cm. The carpenter actually made the desk 60cm by 35cm. 

(a) Calculate the percentage error in the (i) length and the breadth ; (ii) area of the table top.

(b) Find the product of the two errors in a(i).