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? Also, which statement is correct? (1 point) Responses x = approximately 24.5 yards; from the top of the lighthouse to the boat must be the shortest distance x = approximately 24.5 yards; from the top of the lighthouse to the boat must be the shortest distance x = 225 feet; the distance from the lighthouse to the ship must be the longest distance x = 225 feet; the distance from the lighthouse to the ship must be the longest distance x = 15 ft; the distance from the top of the lighthouse to the ship must be the longest distance x = 15 ft; the distance from the top of the lighthouse to the ship must be the longest distance x = 15 ft; the distance from the lighthouse to the ship must be the shortest distance x = 15 ft; the distance from the lighthouse to the ship must be the shortest distance Skip to navigation
To find the horizontal distance from the lighthouse to the ship, we can use the Pythagorean theorem, which states that for a right triangle, the square of the hypotenuse (c, the longest side) is equal to the sum of the squares of the other two sides (a and b).
In this case, the lighthouse's height (a) is 20 ft and the length of the beam (b) is 25 ft. We are looking for the horizontal distance (c).
So, c^2 = 20^2 + 25^2
c^2 = 400 + 625
c^2 = 1025
c = sqrt(1025)
c ≈ 32.02 ft
Therefore, the correct statement is:
x = approximately 32.02 ft; the distance from the lighthouse to the ship must be the longest distance