WAEC 2022 · Paper 2 · Q3

1. Draw the tower $AO$ (110 m) and the building $BC$ on the same ground, with the engineer at the top $O$ of the tower.
2. From $O$, draw a horizontal line across to the building.
3. The angles are measured up ($38^\circ$) and down ($22^\circ$) from it.

(a)

1. The foot of the building is 110 m below the horizontal, at an angle of depression of $22^\circ$: $\tan 22^\circ = \frac{110}{d}$, so $d = \frac{110}{0.4040} \approx 272.3$ m.

(b)

1. Above the horizontal, the top of the building rises $d\tan 38^\circ \approx 272.3 \times 0.7813$
   $\approx 212.7$ m.
2. So the building is $110 + 212.7 = 322.7$ m high.