The distance between ship and base of light house is 514.69 feet
Solution:
Given that, From the top of a 240-ft lighthouse, the angle of depression to a ship in the ocean is 25°
The figure for the problem is attached below
ABC is a right angled triangle
AB = height of light house = 240 feet
BC = distance between ship and base of light house
Angle of depression = 25 degrees
By using defintion of tan,
[tex]tan \theta = \frac{opposite}{adjacent}[/tex]
In right angled triangle, ABC,
Opposite = AB and adjacent = BC
[tex]tan\ 25 = \frac{240}{BC}\\\\0.4663 = \frac{240}{BC}\\\\BC = 514.69[/tex]
Thus distance between ship and base of light house is 514.69 feet
