AA' and BB' denote the height of the plane from the ground.
∴ AA' = BB' = 2500 m
From △OAA'
tan 45° = \(\frac{AA'}{OA'}\)
\(1=\frac{AA'}{OA'}\)
OA' = AA' = 2500 m
From △OBB'
tan 30° = \(\frac{BB'}{OB'}\)
\(\frac 1{\sqrt 3}=\frac{BB'}{OB'}\)
OB' = √3 BB' = 2500√3 m
Distance covered by the plane from A to B is AB or A'B'
⇒ A'B' = OB' – OA'
= (2500√3 − 2500)
= 2500(√3 − 1)
=2500(1.73 − 1)
= 2500 × 0.73
= 1825 m
Time taken by the plane in moving from A to B = 15 seconds
Speed of the plane = \(\frac{1825}{15}\)
= 121.66 ms−1