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A robot arm is programmed to draw a regular octagon. What is the turning angle (exterior angle) required at each vertex if the robot always turns in the same direction (e.g., left) to complete the shape?
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A small rover starts at coordinate (0,0) on a grid. It moves 40 units East (positive x-direction), then turns $90^\circ$ to move North (positive y-direction) and travels 30 units. What are the final (x,y) coordinates of the rover?
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An automated cutting machine needs to cut a rectangular piece of material with a length of 120 mm and a width of 80 mm. The cutter starts at one corner and traces the entire perimeter.
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What is the total distance the cutter travels to complete the perimeter?
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If the cutter makes $90^\circ$ turns at each corner, what is this angle in radians? (Use $\pi \approx 3.14159$)
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A design requires drawing a regular polygon where the external turning angle at each vertex is $30^\circ$. How many sides does this polygon have?
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A mapping system needs to calculate the direct distance between two survey points. Point A is at (2, 5) and Point B is at (10, 11). Calculate the straight-line distance between Point A and Point B.