Question

an aeroplane at a height of 600 passes vertically above another aeroplane at an instant when their angles of elevation at the same of jogging. Are 60 degree and 45 degree respectively how many metres higher is the one from the another​

Answer 1

Mate your answer,

Let the aeroplanes are at point A and D respectively. Aeroplane A is flying 600 m above the ground.

So, AB=600

∠ACB=60°, ∠DCB=45°

From △ABC, we have

$\frac{AB}{BC}$  = tan 60°  

⇒ BC = $\frac{600}{\sqrt{3} }$  = $200\sqrt{3}$

From △DCB,

$\frac{DB}{BC}$ = tan 45°  ⇒ DB = $200\sqrt{3}$

Since, the distance AD = AB − BD = 600 − $200\sqrt{3}$

AD = 200 (3 −  $\sqrt{3}$) = 200 (3 − 1.7321) = 253.58 m

Hence, the distance between the two aeroplanes is 253.58 m.