The captain of a ship at point A and sailing toward point B observes a lighthouse at L and finds angle LAC to be 36*30'. After sailing 5 km to B, he observes angle LBC to be 73*. How many kilometers is position B from the lighthouse?

The distance between B and lighthouse is 3.8688 km

Step-by-step explanation:

Given:

The angle made from ship to lighthouse is 36.5 degrees

and that of point B is 73 degrees.

To Find:

Distance  Between Point B and Lighthouse

Solution:

Consider a triangle LAB(Refer the attachment )

And Point C is on the line AB as A i.e. ship is sailing to B

So C is at 5 km from A.

Now In triangle LAC,

Using Trigonometry Functions as ,

tan(36.5)=LC/AC

LC=tan(36.5)*AC

=0.7399*5

=3.6998 km

Now In triangle LBC,

As,

Sin(73)=LC/LB

LB=LC/(Sin(73))

=3.6998/0.9563

=3.8688 km

LB=3.8688 km