To find the height above the ground when you rotate through an angle of $\theta = 115^\circ$ on a Ferris wheel with a radius $b = 26$ feet, we can use trigonometric functions.

The height $h$ above the ground can be calculated using the formula:

$h = b \cdot (1 - \cos(\theta))$

where:

• $b$ is the radius of the Ferris wheel,
• $\theta$ is the angle of rotation in degrees.

Since the center of the Ferris wheel is at a height of $b$ from the ground, we need to account for this by adding the height from the center to the ground.

1. Calculate the height above the center:

$h_{\text{above center}} = b \cdot \cos(115^\circ)$

2. Calculate the total height above ground:

$h = b + h_{\text{above center}} = b - b \cdot \cos(115^\circ)$

Now substituting $b = 26$ feet:

$h = 26 - 26 \cdot \cos(115^\circ)$

Calculating $\cos(115^\circ)$:

$\cos(115^\circ) \approx -0.422618$

So,

$h = 26 - 26 \cdot (-0.422618) \approx 26 + 10.982068 = 36.982068$

Thus, the height above the ground when the Ferris wheel car halts is approximately:

$h \approx 36.98207 \text{ feet}$

Final Answer:

The height above the ground is $36.98207$ feet.

Would you like more details or have any questions? Here are some related questions you might consider:

1. How does the height change if the angle of rotation is different?
2. What would be the height if the radius of the Ferris wheel were increased?
3. Can you calculate the height at another angle, say $180^\circ$?
4. How does the position on the Ferris wheel affect the overall experience?
5. What are the implications of this calculation for safety in amusement rides?

Tip: Always ensure to convert angles to radians if you're using functions that require it, as some programming environments use radians by default.