A tourist looks out from the crown of the Statue of Liberty, approximately 250 feet above the ground. The tourist sees a ship coming into the harbor and measures the angle of depression as 18 degrees. Find the distance from the base of the statue to the ship to the nearest foot.
To find the distance from the base of the statue to the ship, we can use trigonometry.
Let x be the distance from the base of the statue to the ship.
We have a right triangle with the angle of depression being 18 degrees and the height of the statue being 250 feet. The opposite side is the height of the statue (250 feet) and the adjacent side is the distance from the base of the statue to the ship (x).
Using the tangent function:
tan(18 degrees) = 250/x
Solving for x:
x = 250 / tan(18 degrees)
x ≈ 738.37 feet
Therefore, the distance from the base of the statue to the ship is approximately 738 feet.