WAEC 2020 · Paper 2 · Q8

(a)
In an isosceles triangle $ABC$ , $|AB| = |AC| = 6\text{ cm}$ and $\angle BAC = 130^\circ$ . Find, correct to two significant figures, the: (i) $|BC|$ ; (ii) area of the triangle $ABC$ .
Separate values with commas, e.g. 3, −2
(b)
On a circular park with diameter of $50.0\text{ m}$ , there are 10 lamps whose bases are circles with radius $0.5\text{ m}$ . The entire area of the park is covered with grass except the bases of the lamps. Calculate the area of the park covered by the grass. $\left[\text{Take }\pi = \frac{22}{7}\right]$

Worked solution (try it first)

Two sides and the angle between them: cosine rule.
$|BC|^2 = 6^2 + 6^2 - 2(6)(6)\cos 130^\circ$
$= 72 + 72(0.6428)$
$\approx 118.28$ , so $|BC| \approx 10.88$ , which is 11 cm to two significant figures.

Area $= \frac12 \times 6 \times 6 \times \sin 130^\circ$
$\approx 18 \times 0.7660$
$\approx 13.79$ , which is 14 cm² to two significant figures.

The park has radius 25 m: area $= \frac{22}{7} \times 25^2$
$\approx 1964.29\text{ m}^2$ .
Each lamp base has radius 0.5 m: 10 bases cover $10 \times \frac{22}{7} \times 0.5^2 \approx 7.86\text{ m}^2$ .
Grass $= 1964.29 - 7.86$
$\approx 1956.43\text{ m}^2$ .