For the given right triangle we have:
SL = 23.25km
TL = 12.66km
How far is the ship from the lighthouse?
We know an angle and the adjacent cathetus to that angle, the distance between the ship and the lighthouse is the other cathetus of the right triangle, then we can use the trigonometric relation:
cos(33°) = 19.5km/SL
Solving for LT, we get:
SL = 19.5km/cos(33°)= 23.25km
Now, SL is the hypotenuse of the triangle. Remember that the Pythagorean theorem says that the sum of the squares of the catheti is equal to thes square of the hypotenuse.
Then:
ST² + TL² = SL²
(19.5)² + TL² = (23.25)²
TL = √( (23.25)² - (19.5)² )
TL = 12.66km