Two observers Abu and Badu, 46 m apart, observe a bird on a vertical pole from the same side of the bird. The angles of elevation of the bird from Abu's and Badu's eye are 40º and 48º respectively. If at the foot of the pole Abu and Badu are on same horizontal;

(a) illustrate the information in a diagram;

(b) calculate, correct to one decimal place, the height of the pole.

The diameter of a circle centre O is 26 cm. If a chord \(\overline{PQ}\) is drawn such that it is 5 cm from O to the centre of the chord, calculate, correct to the nearest whole number, the 

(a)\(\angle\)POQ

(b) Area of the minor segment formed by the chord \(\overline{PQ}\). [take \(\pi\) = \(\frac{22}{7}\)]

(a) In a man's will, he gave \(\frac{2}{5}\) of the total acres of the farm to the wife and \(\frac{1}{3}\) of what is left to the family. The rest of the farm was to be shared amongst his three children in the ratio 3: 5: 2. Given that, the child who had the least share received 8 acres, calculate the:

(i) total acres the man left.

(ii) number of acres the wife received.

(b) The price of a Television set is $1,600.00. It can be purchased by a deposit of $400.00 and the rest of the amount paid by 12 monthly installments at 25% per annum simple interest. If the Television set is purchased by installment, find the total cost.

(a) Find the equation of the line that passes through the origin and the point of intersection of the lines \( x + 2y = 7 \) and \( x - y = 4 \). (b) The ratio of an interior angle to an exterior angle of a regular polygon is 4: 1. Find the: (i) number of sides; (ii) value of the exterior angle; and (iii) sum of the interior angles of the polygon.

(a) In the diagram above, \(\overline{PR}\) is a tangent to the circle O at Q. \(\angle\)POQ = 56º and  \(\overline{PO}\) intersect  \(\overline{SO}\) at V such that \(\angle\)SVP = 109º. Calculate: (i) \(\angle\)TQP (ii) \(\angle\)QTS

(b) Simplify \(\frac{2n^2 - 3n - 2 }{2n^2 + 3n + 1} \times \frac{n^2 - 1}{n^2 - 4}\)