To determine the measure of the central angle [tex]\(\angle PQR\)[/tex] in a traffic circle, let's first understand the steps involved in the calculation.
1. Identify the path length: The car travels along a path of 296 feet.
2. Understand the circle geometry:
- The perimeter (circumference) of the circle is given by [tex]\(C = 2\pi r\)[/tex]. Here, for simplicity, we are assuming the radius [tex]\(r = 1\)[/tex], making the circumference [tex]\(C = 2\pi \cdot 1 = 2\pi\)[/tex] feet.
3. Calculate the angle in radians:
- The length of the path (arc length) is 296 feet. To find the corresponding angle in radians, use the ratio of the arc length to the circumference:
[tex]\[
\text{angle in radians} = \frac{\text{arc length}}{\text{circumference}} = \frac{296}{2\pi}
\][/tex]
This simplifies to approximately 47.11 radians.
4. Convert the angle from radians to degrees:
- To convert radians to degrees, use the formula: [tex]\(\text{degrees} = \text{radians} \times \frac{180}{\pi}\)[/tex].
- Thus, the angle in degrees is:
[tex]\[
\text{angle in degrees} = 47.11 \times \frac{180}{\pi} \approx 2699.20 \text{ degrees}
\][/tex]
5. Round to the nearest whole number:
- Finally, rounding 2699.20 degrees to the nearest whole number gives us 2699 degrees.
Therefore, the measure of [tex]\(\angle PQR\)[/tex] is approximately [tex]\(2699\)[/tex] degrees.
The measure of [tex]\(\angle PQR\)[/tex] is approximately [tex]\(2699\)[/tex].
