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Точки і лежать на сфері із центром , діаметр якої дорівнює . Знайдіть відрізок , якщо трикутник є прямокутним.
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Q. Точки і лежать на сфері із центром , діаметр якої дорівнює . Знайдіть відрізок , якщо трикутник є прямокутним.
- Identify Given Information: Identify the given information and the property that will be used to solve the problem.We are given that the diameter of the sphere is , which means the radius is half of that, so . We also know that triangle is a right triangle with the right angle at . By the Pythagorean theorem, the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the longest side (hypotenuse).
- Apply Pythagorean Theorem: Apply the Pythagorean theorem to triangle . Since is the center of the sphere and and lie on the sphere, and are radii of the sphere. Therefore, . is the hypotenuse of the right triangle . Using the Pythagorean theorem: .
- Substitute and Solve: Substitute the known values into the Pythagorean theorem and solve for . becomes ...
- Find Length of CD: Find the length of CD by taking the square root of both sides of the equation.....
- Check for Errors: Check the result for any mathematical errors. The calculations are correct, and the use of the Pythagorean theorem is appropriate for a right triangle. No math errors are present.
