Respuesta :
Answer:
The distance apart of the two planes is either 100.45 km or 64.40 km
Step-by-step explanation:
The given parameters are;
The angle of elevation of the plane from the two radar stations are; 20° and 59°
The altitude of the plane = 30 km
The horizontal distance from each of the radar stations from the plane is given as follows;
[tex]tan(\theta) = \dfrac{Altitude \ of \ the \ plane}{The \ horizontal \ distance \ of \ radar \ station \ from \ the \ plane}[/tex]
Therefore, we have;
[tex]The \ horizontal \ distance \ of \ radar \ station \ from \ the \ plane = \dfrac{Altitude \ of \ the \ plane}{tan(\theta)}[/tex]For each of the given radar stations, and their elevations, we have;
[tex]The \ horizontal \ distance \ of \ the \ 1st \ radar \ station \ from \ the \ plane = \dfrac{30 \ km}{tan(20^{\circ})}[/tex]
[tex]The \ horizontal \ distance \ of \ the \ 2nd \ radar \ station \ from \ the \ plane = \dfrac{30 \ km}{tan(59^{\circ})}[/tex]
The distance between the two radar stations, d = The sum of their horizontal distances from the plane
Therefore;
[tex]d = \dfrac{30 \ km}{tan(20^{\circ})} + \dfrac{30 \ km}{tan(59^{\circ})} \approx 100.45 \ km[/tex]
However, when the radar stations are on the same side, we have;
The distance between the two radar stations, dₓ = The difference of their horizontal distances from the plane
[tex]d_x = \dfrac{30 \ km}{tan(20^{\circ})} - \dfrac{30 \ km}{tan(59^{\circ})} \approx 64.40 \ km[/tex]
The distance apart of the two planes is either 100.45 km or 64.40 km
