A dock is located 24 km directly east of a lighthouse. A sailboat is directly north of the lighthouse. The sailboat is 25 km from the dock. How far away from the lighthouse is the sailboat?
Another nonsense answer by the bot.
x^2 + 24^2 = 25^2
x^2 = 625 - 576
x^2 = 49
x = 7
The sailboat is 7 km away from the lighthouse
To find the distance between the sailboat and the lighthouse, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the distance from the sailboat to the lighthouse forms the hypotenuse of a right triangle, while the distance from the dock to the lighthouse and the distance from the sailboat to the dock form the other two sides.
Using the Pythagorean theorem, we can calculate the distance from the sailboat to the lighthouse as follows:
Distance from the sailboat to the lighthouse = √((Distance from the dock to the lighthouse)^2 - (Distance from the sailboat to the dock)^2)
Plugging in the given values:
Distance from the sailboat to the lighthouse = √((24 km)^2 - (25 km)^2)
Simplifying further:
Distance from the sailboat to the lighthouse = √(576 km^2 - 625 km^2)
Distance from the sailboat to the lighthouse = √(-49 km^2)
Since square roots of negative numbers are not defined in the real number system, it is not possible to determine the distance between the sailboat and the lighthouse based on the given information.
To find out how far away from the lighthouse the sailboat is, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right 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 other two sides.
In this case, let's assume the distance between the sailboat and the lighthouse is 'x' km. We can create a right triangle with the distance between the dock and the lighthouse as one side and the distance between the sailboat and the lighthouse as another side. The hypotenuse will be the straight line distance between the dock and the sailboat.
Using the Pythagorean theorem, we have the following equation:
x^2 = (24 km)^2 + (25 km)^2
To solve this equation, we need to square the values of 24 km and 25 km, and then add them. Finally, we can take the square root of both sides of the equation to find the value of 'x':
x = sqrt((24 km)^2 + (25 km)^2)
Calculating this, we get:
x ≈ sqrt(576 km^2 + 625 km^2)
x ≈ sqrt(1201 km^2)
x ≈ 34.67 km
Therefore, the sailboat is approximately 34.67 km away from the lighthouse.