Answer: The distance between them is 230.65 miles.
Step-by-step explanation:
Since we have given that
Speed of plane A (b) = 200 miles per hour
Speed of plane B (c) = 300 miles per hour
Angle between them = 50°
So,
We will use the "Cosine formula", we get
\(a^2=b^2+c^2-2bc\cos A\\\\a^2=200^2+300^2-2\times 200\times 300\cos 50\textdegree\\\\a^2=40000+90000-120000\cos 50\textdegree\\\\a^2=130000-120000\times 0.64\\\\a^2=130000-76800\\\\a^2=53200\\\\a=\sqrt{53200}\\\\a=230.65\ miles\ per\ hour\)
So, distance between the two planes after one hour will be
\(Distance=\frac{Speed}{time}=\frac{230.65}{1}=230.65\ miles\)
So, the distance between them is 230.65 miles.
