An aeroplane flying horizontally 1 km above the ground is observed at an elevation of 60V After a flight - Maths - Some Applications of Trigonometry

Question

An aeroplane flying horizontally 1 km above the ground is
observed at an elevation of 60 V After a
flight of 10 seconds, its angle of elevation is observed to be
30 V from the same point on the ground
Find the speed of the aeroplane in km/hour

Ayush Jha · Accepted Answer

We have

In triangle ABC $\tan 60^{0} = \frac{1}{x} \sqrt{3} = \frac{1}{x} x = \frac{1}{\sqrt{3}}$ Now in triangle BED, $\tan 30^{o} = \frac{1}{x + y} \frac{1}{\sqrt{3}} = \frac{1}{\frac{1}{\sqrt{3}} + y} \frac{1}{\sqrt{3}} + y = \sqrt{3} y = \frac{2}{\sqrt{3}} k m$ So the speed of the aeroplane is $= \frac{\frac{2}{\sqrt{3}} (60) (60)}{10} = \frac{720}{\sqrt{3}} = 415 69 k m / h r$

An aeroplane flying horizontally 1 km above the ground is observed at an elevation of 60 V . After a flight of 10 seconds, its angle of elevation is observed to be 30 V from the same point on the ground. Find the speed of the aeroplane in km/hour.