(a) A tower and a building stand on the same horizontal level. From the point P at the bottom of the building, the angle of elevation of the top, T of the tower is 65°. From the top Q of the building, the angle of elevation of the point T is 25°. If the building is 20m high, calculate the distance PT.
(b) Hence or otherwise, calculate the height of the tower. [Give your answers correct to 3 significant figures].
Explanation
(a)
(< QPB = 90° – 65° = 25°)
Also, (< TQP = 90° + 25° = 115°)
(therefore < QTP = 180° – (25° + 115°) = 40°)
Using sine rule, (frac{PQ}{sin 40°} = frac{PT}{sin 115°})
(PT = frac{20 sin 115°}{sin 40°} = frac{20 sin 65°}{sin 40°})
= (28.199m approxeq 28.2m) (to 3 sig. fig)
(b) Height of the tower = ST
(sin 65 = frac{ST}{PT} = frac{ST}{28.199})
(ST = 28.199 times sin 65° = 25.557m)
(approxeq 25.6m) (to 3 sig. figs)