An aeroplane when flying at a height of 400 m from the ground passes vertically above another aeroplane at an - Maths - Some Applications of Trigonometry

Question

An aeroplane when flying at a height of 400 m from the ground
passes vertically above another aeroplane at an instant when the
angle of elevation of 2 planes from the same point on the ground
are 60degree and 45 degree Find the vertical distance btw the
aeroplane at that instant

Neha Sethi · Accepted Answer

Let A and B be the positions of two Aeroplanes, when B is vertically below A  In ΔCDB,tan45°=BCCD⇒1=BCCD⇒CD=BC⇒CD=400 m   as BC=400 mIn △ADCtan60°=ACCD3=AB+BCCD⇒3=AB+400400⇒4003=AB+400⇒AB=4003-400 m⇒AB=4003-1m
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An aeroplane when flying at a height of 400 m from the ground passes vertically above another aeroplane at an instant when the angle of elevation of 2 planes from the same point on the ground are 60degree and 45 degree. Find the vertical distance btw the aeroplane at that instant