Bearings

[Andreaaiii]

Hi,

I need some help on solving this question about Bearings.

"Jacob is walking north along a straight road when he spots a tower in a field to his right on a bearing of 018 degrees. After walking another 240 meters he notices the tower is now on a bearing of 066 degrees. If he continues walking north, how close will he pass to the tower?"

Thank you so much. I tried working it out, but I don't understand the problem so I'm not sure if my diagram is drawn correctly.

 

[Ishuda]

Hi,

I need some help on solving this question about Bearings.

"Jacob is walking north along a straight road when he spots a tower in a field to his right on a bearing of 018 degrees. After walking another 240 meters he notices the tower is now on a bearing of 066 degrees. If he continues walking north, how close will he pass to the tower?"

Thank you so much. I tried working it out, but I don't understand the problem so I'm not sure if my diagram is drawn correctly.

Bearing is measured from North being zero and positive clock wise. Let N be on a line perpendicular to (the extended) line AB and indicate the direction North, the tower be point T, the initial sighting point A and the second sighting point B:
N__________________T
|
|
B
|
|
A
Draw a triangle TBA. The angle between AT & AB is 18 degrees. The angle between lines BT & BN is 66 degrees. So what is the angle between lines AB and BT? What are the third angles between lines BT and NT and lines BT and AT? Having answered that, you have an angle, side [line AB is of length 240 m], angle. So, law of sines for side BT. Given that and the angles of triangle BTN, what is NT?