Question

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)

x = 225 feet; the distance from the lighthouse to the ship must be the longest distance

x = approximately 24.5 yards; from the top of the lighthouse to the boat must be the shortest 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
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Answer 1

Use the Pythagorean theorem: x^2 + 20^2 = 25^2, so x = sqrt(25^2 − 20^2) = sqrt(625 − 400) = sqrt(225) = 15 ft.

Since the three distances are 15 ft (horizontal), 20 ft (vertical), and 25 ft (beam), the beam (top of lighthouse to ship) is the longest. So x = 15 ft and the correct choice is the one stating the top-to-ship distance is the longest (the third option).