Question

Aeroplane flying horizontally 1.2 km above the ground is observed at an elevation angle of 60 after 15 sec its elevation angle is observed to be 30 degree find the speed of the aeroplane in km per hour

Answer 1

$\large{\mathsf{Note:-}}$ Diagram of this question attached in attachment file.

$\mathfrak{Question:-}$

Aeroplane flying horizontally 1.2 km above the ground is observed at an elevation angle of 60 after 15 sec its elevation angle is observed to be 30 degree find the speed of the aeroplane in km per hour.

$\mathfrak{Solution:-}$

In triangle ABC,

$\bold{tan\; 60^{\circ} = \frac{1}{x}}$

$\bold{\sqrt{3} = \frac{1}{x}}$

$\bold {x = \frac{1}{\sqrt{3}}}$

Now in Triangle BED,

$\bold{tan\; 30^{\circ} = \frac{1}{x+y}}$

$\bold{\frac{1}{\sqrt{3}} = \frac{1}{\frac{1}{\sqrt{3}}+y}}$

$\bold{\frac{1}{\sqrt{3}} + y = \sqrt{3}}$

$\bold{y = \frac{2}{\sqrt{3}}\; km}$

So the speed of aeroplane is

$\bold{= \frac{\frac{2}{\sqrt{3}} (60)\, (60)}{10}}$

$\bold{=\frac{720}{\sqrt{3}}}$

$\bold{\boxed{\boxed{\bold{= 415.69\; km/hr}}}}$