Theory question 103
Trigonometry(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.)
Show the model answer
Model answer
(a) In triangle PQT: ∠QPT = 90° − 65° = 25°, ∠PQT = 90° + 25° = 115°, so ∠PTQ = 40°
Sine rule: PT/sin 115° = 20/sin 40°
PT = 20 × 0.9063/0.6428 = 28.2 m
(b) Height of tower = PT sin 65° = 28.2 × 0.9063 = 25.6 m
Explanation
Sketch the building PQ and tower first; the key is finding the angles of triangle PQT.