A man standing on a lighthouse at a height of 124 feet sights two boats directly in front of him. One is at an angle of depression of 62°, and the other is at an angle of depression of 33°. Identify the distance between the two boats. Round your answer to the nearest foot.

Answer:[tex]125\ ft[/tex]Step-by-step explanation:see the attached figure to better understand the problemstep 1In the right triangle ABC find the length side BCwe know that[tex]tan(62\°)=\frac{124}{BC}[/tex][tex]BC=\frac{124}{tan(62\°)}[/tex]step 2In the right triangle ABD find the length side BDwe know that[tex]tan(33\°)=\frac{124}{BD}[/tex][tex]BD=\frac{124}{tan(33\°)}[/tex]step 3we know thatThe distance between the two boats is the length side CD[tex]CD=BD-BC[/tex]substitute the values  [tex]CD=\frac{124}{tan(33\°)}-\frac{124}{tan(62\°)}=125\ ft[/tex]