Answer:
The distance between the two planes is 3.65 mi
Step-by-step explanation:
The locations, given in polar coordinates, for two planes approaching an airport are (4 mi, 12º) and (3 mi, 73º).
Please see the attachment for figure.
OP=3 mi
OQ=4 mi
∠POQ = 73° - 12° = 61°
Using cosine law:
[tex]a^2=b^2+c^2-2bc\cos A[/tex]
[tex]PQ^2=OP^2+OQ^2-2\cdot OP\cdot OQ\cos POQ[/tex]
[tex]PQ^2=4^2+3^2-2\cdot 4\cdot 3\cos 61^\circ[/tex]
[tex]PQ^2=13.36[/tex]
[tex]PQ=3.65\text{ mi}[/tex]
Hence, The distance between the two planes is 3.65 mi
