Question

Find the horizontal distance needed for the ramp. Round to the nearest hundredth (2 decimal places).
84ft is the ramp length 4.8 is ramp run

Answer 1

To find the horizontal distance of the ramp, we can use the Pythagorean theorem. In this case, the ramp length represents the hypotenuse of a right triangle, and the ramp run represents one side. We can denote the ramp length as \( c \) (hypotenuse) and the ramp run as \( a \) (one leg), while \( b \) will be the other leg (the vertical height).

The Pythagorean theorem is given by:

\[
c^2 = a^2 + b^2
\]

In your case:

- \( c = 84\, \text{ft} \) (ramp length)
- \( a = 4.8\, \text{ft} \) (ramp run)

We need to find \( b \), which can be rearranged from the equation as follows:

\[
b^2 = c^2 - a^2
\]

Substituting the values into the equation:

\[
b^2 = 84^2 - 4.8^2
\]

Calculating \( 84^2 \):

\[
84^2 = 7056
\]

Calculating \( 4.8^2 \):

\[
4.8^2 = 23.04
\]

Now substituting back into the equation:

\[
b^2 = 7056 - 23.04
\]
\[
b^2 = 7032.96
\]

Now take the square root of both sides to find \( b \):

\[
b = \sqrt{7032.96} \approx 83.78\, \text{ft}
\]

Thus, the horizontal distance needed for the ramp is approximately ***83.78 feet*** when rounded to two decimal places.