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.
2.0 inches
10.0 inches
16.9 inches
69.2 inches
2.0 inches
10.0 inches
16.9 inches
69.2 inches
Answers
GPT-4o mini
To solve the problem, we can use the Pythagorean theorem.
We have a right triangle formed by the ramp, the height of the ramp, and the distance along the ground. The lengths of the sides of the triangle are:
- The length of the ramp (hypotenuse): 72 inches
- The horizontal distance along the ground: 70 inches
- The height of the ramp above the ground (which we need to find): \( h \) inches
According to the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
where \( a \) is the height of the ramp, \( b \) is the distance along the ground, and \( c \) is the length of the ramp.
Substituting the known values into the equation:
\[
h^2 + 70^2 = 72^2
\]
Calculating \( 70^2 \) and \( 72^2 \):
\[
h^2 + 4900 = 5184
\]
Now, we can isolate \( h^2 \):
\[
h^2 = 5184 - 4900
\]
\[
h^2 = 284
\]
Now, taking the square root of both sides to find \( h \):
\[
h = \sqrt{284} \approx 16.9
\]
Therefore, the height of the ramp above the ground is approximately \( 16.9 \) inches when rounded to the nearest tenth of an inch.
The answer is **16.9 inches**.
We have a right triangle formed by the ramp, the height of the ramp, and the distance along the ground. The lengths of the sides of the triangle are:
- The length of the ramp (hypotenuse): 72 inches
- The horizontal distance along the ground: 70 inches
- The height of the ramp above the ground (which we need to find): \( h \) inches
According to the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
where \( a \) is the height of the ramp, \( b \) is the distance along the ground, and \( c \) is the length of the ramp.
Substituting the known values into the equation:
\[
h^2 + 70^2 = 72^2
\]
Calculating \( 70^2 \) and \( 72^2 \):
\[
h^2 + 4900 = 5184
\]
Now, we can isolate \( h^2 \):
\[
h^2 = 5184 - 4900
\]
\[
h^2 = 284
\]
Now, taking the square root of both sides to find \( h \):
\[
h = \sqrt{284} \approx 16.9
\]
Therefore, the height of the ramp above the ground is approximately \( 16.9 \) inches when rounded to the nearest tenth of an inch.
The answer is **16.9 inches**.