Answer:
They would be 1525.48 miles apart.
Step-by-step explanation:
Given,
Speed of first plane = 250 miles/hr,
∵ Distance = speed × time,
So, the distance covered by the plane after 3 hours = 250 × 3 = 750 miles,
Similarly, speed of second plane = 300 miles/hr,
Distance covered by the plane after 3 hours = 300 × 3 = 900 miles,
Now, first plane is going east direction while other one is going towards southwest direction,
That is, the angle between them = 90° + 45° = 135°,
if x be the distance between them after 3 hours,
Using cosine law,
[tex]x^2 = 750^2 + 900^2 - 2\times 750\times 900\times \cos 135^{\circ}[/tex]
[tex]x^2 = 562500 + 810000 - 1350000\cos 135^{\circ}[/tex]
[tex]x^2 = 2327094.1546[/tex]
[tex]\implies x = \sqrt{2327094.1546}\approx 1525.48[/tex]
Hence, they would be 1525.48 miles apart after 3 hours.
