Name:
ID: A
40. Thomas used a 2.6-m-long ramp to move furniture into a moving van. If the bottom of the ramp is $2.0 \mathrm{~m}$ from the back of the moving van, what is the angle between the ramp and the ground, to the nearest degree?

Step 1 ：Let \(x\) be the angle between the ramp and the ground. We can use the cosine formula to find the angle: \[\cos x = \frac{adjacent}{hypotenuse}\]

Step 2 ：In this case, the adjacent side is the distance from the bottom of the ramp to the back of the moving van, which is \(2.0\mathrm{~m}\), and the hypotenuse is the length of the ramp, which is \(2.6\mathrm{~m}\).

Step 3 ：Plugging these values into the cosine formula, we get: \[\cos x = \frac{2.0}{2.6}\]

Step 4 ：Now, we can use the inverse cosine function to find the angle \(x\): \[x = \arccos\left(\frac{2.0}{2.6}\right)\]

Step 5 ：Calculating the angle, we get: \[x \approx 38.21^\circ\]

Step 6 ：Rounding to the nearest degree, we have: \[x \approx \boxed{38^\circ}\]