Answer:
The ship is 25.54 miles far from the light house.
Step-by-step explanation:
It is given that A boat travels 26 miles East from a lighthouse then changes direction traveling 15° South of West for 13 miles that is :
BC=c, BA=26 miles and CA=13miles
Then, applying the cosine formula in ΔABC, we get
[tex](BC)^2=(BA)^2+(AC)^2-2(BA)(AC)cos15^{\circ}[/tex]
⇒[tex]c^2=(26)^2+(13)^2-2(26)(13)(0.965)[/tex]
⇒[tex]c^2=676+169-675(0.965)[/tex]
⇒[tex]c^2=652.34[/tex]
⇒[tex]c=25.54miles[/tex]
Therefore, the ship is 25.54 miles far from the light house.
