Consider a diving board that is 10
feet above a pool.
Image_9274
If the ladder is 5
feet away from the base of the diving board, approximately how tall is the ladder?
Responses
9
feet
9 feet
11
feet
11 feet
15
feet
15 feet
17
feet
We can solve this problem using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the diving board acts as one side of the right triangle, the ladder acts as the hypotenuse, and the distance between the base of the diving board and the ladder acts as the other side of the right triangle.
Let's call the height of the ladder h. The distance between the base of the diving board and the ladder is given as 5 feet.
Using the Pythagorean theorem, we have:
h^2 = 10^2 + 5^2
h^2 = 100 + 25
h^2 = 125
Taking the square root of both sides, we find:
h ≈ √125
h ≈ 11.18
So, approximately, the ladder is 11 feet tall.
To find the height of the ladder, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this scenario, the height of the diving board is one side of the right triangle, and the distance between the base of the diving board and the ladder is another side. The ladder itself represents the hypotenuse.
Using the Pythagorean theorem, we can calculate the height of the ladder:
height of diving board^2 + distance between base and ladder^2 = height of ladder^2
Substituting the known values:
10^2 + 5^2 = height of ladder^2
100 + 25 = height of ladder^2
125 = height of ladder^2
To find the square root of 125, we can estimate it as a whole number.
The closest whole number is 11.
Therefore, the height of the ladder is approximately 11 feet.
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square 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 diving board, ladder, and the distance from the base of the diving board to the ladder form a right triangle.
We know that the diving board is 10 feet above the pool, and the ladder is 5 feet away from the base of the diving board. Let's call the height of the ladder "h".
Using the Pythagorean theorem, we can write the equation:
(10^2) + (5^2) = h^2
Simplifying this equation, we get:
100 + 25 = h^2
125 = h^2
To find the value of "h", we need to take the square root of both sides of the equation:
√(125) = √(h^2)
√(125) = h
Now, let's calculate the approximate value of "h":
√(125) = 11.18 feet
Therefore, the ladder is approximately 11 feet tall. So the correct response would be:
11
feet