Question

a moving van ramp is 72 inches in length. the top of the ramp can be adjusted to any height up to 20 inches. the ramp is set so that the distance across the ground from the bottom of the ramp to the ground underneath the top of the ramp is 70 inches. what is the height of the ramp above the ground? round the answer to the nearest tenth of an inch.
16.9 inches
2.0 inches
69.2 inches
10.0 inches

Explanation:

Step1: Use the Pythagorean theorem

Let the height be \(h\), the length of the ramp \(c = 72\) inches, and the base \(b=70\) inches. The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), so \(h=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute values

Substitute \(c = 72\) and \(b = 70\) into the formula: \(h=\sqrt{72^{2}-70^{2}}=\sqrt{(72 + 70)(72-70)}=\sqrt{142\times2}=\sqrt{284}\).

Step3: Calculate the square - root

\(\sqrt{284}\approx16.9\) (rounded to the nearest tenth).

Answer:

16.9 inches