Question

the angle of elevation of an aeroplane flying vertically above the ground as observed from two consecutive stones 1km apart are 45 and 60 the length of the aeroplane above the ground in km is

Answer 1

2.3947 km is the height of aeroplane

Answer 2

Answer:

Length of the aeroplane above the ground is 2.37 km

Step-by-step explanation:

Given: Angles of elevation are 45° and 60°.

          Distance between two points are 1 km

To find: Distance between plane and ground in km, AB

Figure is attached.

In ΔABC,

using trigonometric ratio, we get

$tan\,60=\frac{AB}{AC}$

$AB=\sqrt{3}\times AC$ ..........................(1)

In ΔABD,

using trigonometric ratio, we get

$tan\,45=\frac{AB}{AD}$

$tan\,45=\frac{AB}{AC+BD}$

$AB=1+AC$ ..........................(2)

From (1) and (2)

√3 AC = 1 + AC

$AC=\frac{1}{\sqrt{3}-1}$

Now put this in (1)

$AB=\frac{\sqrt{3}}{\sqrt{3}-1}=\frac{1.73}{1.73-1}=2.37\:km$

Therefore, Length of the aeroplane above the ground is 2.37 km