Final answer:
Using the Pythagorean theorem, we find that the distance from the bottom of the ramp to the dock is approximately 17.29 feet.
Step-by-step explanation:
To find the distance from the bottom of the ramp to the dock, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two legs (a and b) is equal to the square of the hypotenuse (c): a2 + b2 = c2. In this scenario, the ramp is the hypotenuse (c), the height of the dock is one leg (a), and the distance from the bottom of the ramp to the dock is the other leg (b).
Given:
The length of the ramp (hypotenuse) is 18 feet.
The height of the dock (one leg) is 5 feet.
We will solve for the other leg (b).
Step 1: Write down the Pythagorean theorem: a2 + b2 = c2.
Step 2: Plug in the known values: 52 + b2 = 182.
Step 3: Perform the squares: 25 + b2 = 324.
Step 4: Subtract 25 from both sides: b2 = 324 - 25.
Step 5: Calculate the result: b2 = 299.
Step 6: Take the square root of both sides: b = √299.
Step 7: Find that b is approximately 17.29 feet.
Therefore, the distance from the bottom of the ramp to the dock is approximately 17.29 feet.