How far is it from the lighthouse to the ship horizontally if the lighthouse is 20 ft tall and shines a beam to the ship 25 ft long?
The distance from the lighthouse to the ship horizontally can be calculated using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the height of the lighthouse is 20 ft and the length of the beam shining to the ship is 25 ft. Let x be the horizontal distance from the lighthouse to the ship.
Using the Pythagorean theorem, we have:
x^2 = 25^2 - 20^2
x^2 = 625 - 400
x^2 = 225
x = √225
x = 15
Therefore, the distance from the lighthouse to the ship horizontally is 15 ft.