# One boat travelled at 10km/h on a course of 280 degrees. The other boat travelled at 13km/h on a course of 165 degrees. How far part were the boats after 2 h?please expain in detail

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embizze | Certified Educator

Boat A travels at 10km/hr on a course of 280 degrees (this is `10^@` north of due west.)

Boat B travels at 13 km/hr on a course of 165 degrees (this is `15^@` east of south.)

After 2 hours boat A has travelled 20km, and boat B has travelled 26km.

The angle between the boats is `280^@-165^@=115^@` .

Draw a triangle with one side 20, one side 26, and the included angle `115^@` . We can use the Law of Cosines to ind the third side, which is the distance between the boats.

`c^2=20^2+26^2-2(20)(26)cos115^@`

`c^2=1076-1040cos115^@`

`c^2~~1515.52`

`c~~38.93`

**The distance between the boats is approximately 38.93km**