A kite is flying 20
feet high above a turtle. The other end of the string is anchored under a rock that is 15
feet from the turtle.
Image_1929
How long is the string?
Responses
5
feet
5 feet
13
feet
13 feet
25
feet
25 feet
35
feet
To find the length of the string, we can use the Pythagorean theorem. The Pythagorean theorem 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 other two sides.
In this case, the length of the string is the hypotenuse, and the height of the kite and the distance from the turtle to the anchor point under the rock are the other two sides.
Let's calculate it step by step:
1. Square the height of the kite: 20 feet * 20 feet = 400 square feet.
2. Square the distance from the turtle to the anchor point: 15 feet * 15 feet = 225 square feet.
3. Add these two values together: 400 square feet + 225 square feet = 625 square feet.
4. Take the square root of this sum: √625 = 25 feet.
Therefore, the length of the string is 25 feet.
Final Answer: 25 feet.
To calculate the length of the string, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the height of the kite forms one side of a right triangle, the distance from the turtle to the rock forms the other side, and the length of the string forms the hypotenuse.
Using the given information, we can calculate the length of the string:
Distance from the turtle to the rock = 15 feet
Height of the kite = 20 feet
Using the Pythagorean theorem, we have:
Length of the string^2 = Distance^2 + Height^2
Length of the string^2 = 15^2 + 20^2
Length of the string^2 = 225 + 400
Length of the string^2 = 625
Taking the square root of both sides, we get:
Length of the string = √625
Length of the string = 25 feet
Therefore, the length of the string is 25 feet.
To find the length of the string, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the height of the kite (20 feet) represents one side of the triangle, and the distance to the rock (15 feet) represents the other side. The length of the string is the hypotenuse.
Using the Pythagorean theorem:
String length^2 = (Height^2) + (Distance^2)
String length^2 = (20^2) + (15^2)
String length^2 = 400 + 225
String length^2 = 625
Taking the square root of both sides:
String length = √625
String length = 25 feet
Therefore, the length of the string is 25 feet.