Final answer:
To determine the length of the ramp, the Pythagorean theorem is used to calculate the hypotenuse of a right-angled triangle formed by the height and base of the ramp. The length is found to be approximately 6.18 feet when rounded to the nearest hundredth.
Step-by-step explanation:
The student's question involves finding the length of a pet ramp given the top height (1.5 ft) and the bottom distance from the ramp (6 ft). This problem falls within the domain of Mathematics, specifically into the geometry segment concerning the Pythagorean theorem. To find the length of the ramp, a right-angled triangle is considered with 1.5 ft as one leg (height) and 6 ft as the other leg (base). Using the Pythagorean theorem (a² + b² = c²), we can solve for c, the hypotenuse, which is the length of the ramp.
The calculation process is:Calculate the square of both legs: (1.5)² + (6)².
Add the results.
Find the square root of the sum to get the length of the ramp to the nearest hundredth.
Following these steps, the calculation would look like this:
(1.5)² + (6)² = 2.25 + 36 = 38.25
√38.25 ≈ 6.18 ft
So, the length of the ramp is approximately 6.18 feet when rounded to the nearest hundredth.