Question
If the length of the ramp is 16 inches and the vertical rise is 14 inches, what is the possible measurements for the horizontal distance?
Answers
GPT-4o mini
To find the possible horizontal distance for the ramp, we can use the Pythagorean theorem, which states:
\[
c^2 = a^2 + b^2
\]
where \(c\) is the length of the ramp (the hypotenuse), \(a\) is the vertical rise, and \(b\) is the horizontal distance.
Given that the length of the ramp \(c\) is 16 inches and the vertical rise \(a\) is 14 inches, we want to find the horizontal distance \(b\).
Plugging the known values into the equation gives us:
\[
16^2 = 14^2 + b^2
\]
Calculating the squares:
\[
256 = 196 + b^2
\]
Now, subtract 196 from both sides:
\[
256 - 196 = b^2
\]
This simplifies to:
\[
60 = b^2
\]
Taking the square root of both sides gives us:
\[
b = \sqrt{60} \approx 7.75 \text{ inches}
\]
So, the horizontal distance \(b\) is approximately 7.75 inches.
In summary, the horizontal distance for the given ramp dimensions is about 7.75 inches.
\[
c^2 = a^2 + b^2
\]
where \(c\) is the length of the ramp (the hypotenuse), \(a\) is the vertical rise, and \(b\) is the horizontal distance.
Given that the length of the ramp \(c\) is 16 inches and the vertical rise \(a\) is 14 inches, we want to find the horizontal distance \(b\).
Plugging the known values into the equation gives us:
\[
16^2 = 14^2 + b^2
\]
Calculating the squares:
\[
256 = 196 + b^2
\]
Now, subtract 196 from both sides:
\[
256 - 196 = b^2
\]
This simplifies to:
\[
60 = b^2
\]
Taking the square root of both sides gives us:
\[
b = \sqrt{60} \approx 7.75 \text{ inches}
\]
So, the horizontal distance \(b\) is approximately 7.75 inches.
In summary, the horizontal distance for the given ramp dimensions is about 7.75 inches.