Find the horizontal distance needed for the ramp. Round to the nearest hundredth (2 decimal places).

Question

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.