WAEC 2020 · Paper 2 · Q13

A triangular plot of land $ABC$ is such that $|AB| = 85\text{ m}$ , $|BC| = 110\text{ m}$ and $\angle CAB = 60^\circ$ .

(a)
Using a ruler and a pair of compasses only and a scale of 1 cm to 10 m, construct the: (i) triangular plot $ABC$ ; (ii) position of a vertical telegraph post $X$ which is equidistant from $\overline{AC}$ and $\overline{BC}$ and on the perpendicular from $B$ to $\overline{AC}$ .
Model answer
Use only a ruler and a pair of compasses: leave every construction arc visible, because the examiner looks for them. At 1 cm to 10 m, draw $AB = 8.5$ cm and construct $60^\circ$ at $A$ . With centre $B$ and radius 11 cm, cut the arm at $C$ (so $AC \approx 12.4$ cm). Equidistant from $AC$ and $BC$ means the bisector of angle $ACB$ . Draw it, and draw the perpendicular from $B$ to $AC$ . They meet at $X$ . Measured: $|XC| \approx$ 8.8 cm, i.e. about 88 m.
(b)
Find the actual distance from $X$ to $C$ .

The accurate construction (1 unit = 10 m): A(0, 0), B(8.5, 0), C(6.21, 10.76), X(4.84, 2.11).

Worked solution (try it first)

With 1 cm to 10 m: $AB = 8.5$ cm and $BC = 11$ cm.
Draw a base line from $A$ , construct $60^\circ$ at $A$ , and mark $AB = 8.5$ cm on the arm.
With centre $B$ and radius 11 cm, cut the base line at $C$ (so $|AC| \approx 12.4$ cm).