Theory question 112
TrigonometryFrom a horizontal distance of 8.5km, a pilot observes that the angles of depression of the top and base of a control tower are 30° and 33° respectively. Calculate, correct to three significant figures: (i) the shortest distance between the pilot and the base of the control tower; (ii) the height of the control tower.
Show the model answer
Model answer
(i) cos 33° = 8.5/d, so d = 8.5/0.8387 = 10.1km
(ii) Height of pilot above the base = 8.5 tan 33° = 5.520km; above the top = 8.5 tan 30° = 4.907km
Height of tower = 5.520 − 4.907 = 0.612km (612m)
Explanation
Draw one horizontal line from the pilot; both angles of depression are measured from it.