Hornbein
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A screwy problem in basic trigonometry that I thought up.
A pitcher's mound is ten inches high and 18 feet in diameter. Suppose that this is a section of a ball. What is the radius of that ball?
Another way of looking at it is this. You have a large ball. Drill a hole in it ten inches deep. The bottom of the hole is part of a plane that is perpendicular to the shaft. The intersection of that plane with the surface of the ball is a circle with diameter 18 feet. What is the radius of the ball?
Consider a right triangle with legs of 108 inches and ten inches. The arc tangent is 5.29 degrees. So the radius of the sphere is 108"/sin(5.29) + 10" = 98.5 feet.
A pitcher's mound is ten inches high and 18 feet in diameter. Suppose that this is a section of a ball. What is the radius of that ball?
Another way of looking at it is this. You have a large ball. Drill a hole in it ten inches deep. The bottom of the hole is part of a plane that is perpendicular to the shaft. The intersection of that plane with the surface of the ball is a circle with diameter 18 feet. What is the radius of the ball?
Consider a right triangle with legs of 108 inches and ten inches. The arc tangent is 5.29 degrees. So the radius of the sphere is 108"/sin(5.29) + 10" = 98.5 feet.