Question

An aeroplane is flying horizontally, directly towards the city of Melbourne at an altitude of 400 metres. At a given time the pilot views the city lights of Melbourne at an angle of depression of 1.5°. Two minutes later the angle of depression of the city lights is 5°. Find the speed of the aeroplane in km/h, correct to one decimal place.

Please include a diagram

Answer 1

A diagram and review of the basic trig functions will show that the distance d flown by the plane between observations is

d = 400 cot 1.5° - 400 cot 5° = 10700m = 10.7km

10.7km/2min * 60min/hr = 321 km/hr

Hope this helps