Hello, linalg123!

You need a better sketch.

A lighthouse keeper spots a ship sailing away from the shore.

She marks the bearing from North to the ship as and estimates the distance to the ship as 2.4km.

The captain of the ship notes the ship is heading from north.

If the captain similarly estimates the distance to the lighthouse is 2.4km,

what are thepolar coordinatesof the lighthouse in the ship's frame of reference?

The lighthouse is atCode:B C : * : * A :30°* : : * 60° : S o - - - - - D : * 114° : * : * :24°* 2.4 : * : * :* 66° L o - - - - - - - - E

The ship is at

The ship is heading to

But none of this is relevant.

We have:

Using as the origin, the polar coordinates of are:

. . .

Recall that in polar coordinates,

. . is measured from thepositive x-axis,

. . in this instance,