A ship is sailing due west. At a certain time, a lighthouse is observed in the direction N65W. After the ship has travelled 6.8 km, the bearing of the lighthouse becomes N28W as shown in the figure.
(a) How far is the ship from the lighthouse now?
(b) What is the shortest distance between the ship and the lighthouse if the ship continues to sail due west?

Question

A ship is sailing due west. At a certain time, a lighthouse is observed in the direction N65W. After the ship has travelled 6.8 km, the bearing of the lighthouse becomes N28W as shown in the figure.
(a) How far is the ship from the lighthouse now?
(b) What is the shortest distance between the ship and the lighthouse if the ship continues to sail due west?

anonymous · Answer

|dw:1367075240927:dw|

phi · Answer

I think you can use the Law of Sines
|dw:1367087659201:dw|
$$ \frac{x}{\sin25}= \frac{6.8}{\sin37} $$