Question

A boat travels 26 miles East from a lighthouse then changes direction traveling 15(deg) South of West for 13 miles. How far is the ship from the lighthouse? Round to the nearest hundredth

Answer 1

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

$(BC)^2=(BA)^2+(AC)^2-2(BA)(AC)cos15^{\circ}$

⇒$c^2=(26)^2+(13)^2-2(26)(13)(0.965)$

⇒$c^2=676+169-675(0.965)$

⇒$c^2=652.34$

⇒$c=25.54miles$

Therefore, the ship is 25.54 miles far from the light house.