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The figure below is a simplified model of a Ferris wheel with diameter 250 feet. The top of the wheel is 265 feet above the ground. If θ is the central angle formed as a rider moves from position P0 to position P1, find the rider's height above the ground h when θ is 120°.

The figure below is a simplified model of a Ferris wheel with diameter 250 feet. The top of the wheel is 265 feet above the ground. If θ is the central angle formed as a rider moves from position P0 to position P1, find the rider's height above the ground h when θ is 120°.

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The figure below is a simplified model of a Ferris wheel with diameter 250 feet. The top of the wheel is 265 feet above the ground. If θ is the central angle formed as a rider moves from position P0 to position P1, find the rider's height above the ground h when θ is 120°.

The diagram illustrates a circle with a central point and two radii extending from this point. One radius extends vertically downwards to a point labeled \( P_0 \), while the second radius extends at an angle \(\theta\) to a point \( P_1 \). Key elements in the diagram include: 1. **Circle**: The circle represents the path or locus of points equidistant from a central point. 2. **Radius**: The line segment from the center of the circle to any point on its circumference, shown here in two instances: - From the center to \( P_0 \), marked as a vertical blue line. - From the center to \( P_1 \), forming an angle \(\theta\) with the vertical line. 3. **Angle \(\theta\)**: The angle formed between the vertical line (radius to \( P_0 \)) and the radius extending to \( P_1 \). 4. **Height \( h \)**: A vertical red line segment that represents the vertical distance from \( P_1 \) down to the horizontal baseline. This height is perpendicular to the baseline. The diagram likely serves to illustrate concepts involving circular motion, trigonometry, or geometric properties of circles, such as the use of angles and distances within a circle.
Transcribed Image Text:The diagram illustrates a circle with a central point and two radii extending from this point. One radius extends vertically downwards to a point labeled \( P_0 \), while the second radius extends at an angle \(\theta\) to a point \( P_1 \). Key elements in the diagram include: 1. **Circle**: The circle represents the path or locus of points equidistant from a central point. 2. **Radius**: The line segment from the center of the circle to any point on its circumference, shown here in two instances: - From the center to \( P_0 \), marked as a vertical blue line. - From the center to \( P_1 \), forming an angle \(\theta\) with the vertical line. 3. **Angle \(\theta\)**: The angle formed between the vertical line (radius to \( P_0 \)) and the radius extending to \( P_1 \). 4. **Height \( h \)**: A vertical red line segment that represents the vertical distance from \( P_1 \) down to the horizontal baseline. This height is perpendicular to the baseline. The diagram likely serves to illustrate concepts involving circular motion, trigonometry, or geometric properties of circles, such as the use of angles and distances within a circle.
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