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 = 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 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
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 = approximately 24.5 yards; from the top of the lighthouse to the boat must be the shortest distance
To find the horizontal distance (x) from the lighthouse to the ship, we can use the Pythagorean theorem:
x^2 = 25^2 - 20^2
x^2 = 625 - 400
x^2 = 225
x = √225
x = 15 ft
Therefore, the correct statement is:
x = 15 ft; the distance from the lighthouse to the ship must be the shortest distance
COuld you explain the reason?
Of course!
The reason why the distance from the lighthouse to the ship (the horizontal distance, x) must be the shortest distance is because the height of the lighthouse (20 ft) creates a right triangle with the beam of light (25 ft) shining from the lighthouse to the ship.
In a right triangle, the hypotenuse (the longest side, which is the beam of light in this case) is always opposite the right angle. The other two sides, called the legs, are the other two sides of the triangle. So, in this case, the horizontal distance from the lighthouse to the ship (x) is one of the legs of the right triangle.
The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. By applying the Pythagorean theorem, we found that the horizontal distance (x) from the lighthouse to the ship is 15 ft, making it the shortest distance.
Therefore, the statement "x = 15 ft; the distance from the lighthouse to the ship must be the shortest distance" is correct based on the geometric properties of right triangles and the Pythagorean theorem.