Question

The locations, given in polar coordinates, for two planes approaching an airport are (4 mi, 12º) and (3 mi, 73º). Find the distance between the two planes.

Answer 1

Distance formula = sqrt[(4^2 + 3^2) - 2(3×4)cos(73-12)]

sqrt[(25) - 24cos(61)]

sqrt(25 - 11.64)

sqrt(13.36)

final answer = 3.66

Hope this helps!

Answer 2

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:

$a^2=b^2+c^2-2bc\cos A$

$PQ^2=OP^2+OQ^2-2\cdot OP\cdot OQ\cos POQ$

$PQ^2=4^2+3^2-2\cdot 4\cdot 3\cos 61^\circ$

$PQ^2=13.36$

$PQ=3.65\text{ mi}$

Hence, The distance between the two planes is 3.65 mi