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Median on Hypotenuse Formula:
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The median on the hypotenuse of a right-angled triangle is a line segment joining the midpoint of the hypotenuse to its opposite vertex (the right angle vertex). In a right triangle, this median has a special property - its length is exactly half the length of the hypotenuse.
The calculator uses the median formula:
Where:
Explanation: This formula demonstrates that in any right-angled triangle, the median drawn to the hypotenuse is exactly half the length of the hypotenuse itself.
Details: Understanding this relationship is crucial in geometry problems involving right triangles. It's particularly useful in construction, engineering, and various mathematical proofs where right triangles are involved.
Tips: Enter the length of the hypotenuse in meters. The value must be positive and greater than zero. The calculator will automatically compute the median length.
Q1: Why is the median exactly half the hypotenuse?
A: This is a special property of right triangles. The median to the hypotenuse creates two isosceles triangles, making the median equal to half the hypotenuse.
Q2: Does this formula work for all right triangles?
A: Yes, this formula applies to all right-angled triangles regardless of their other dimensions or angles.
Q3: What units should I use?
A: The calculator uses meters, but the formula works with any consistent unit of measurement (cm, mm, inches, etc.).
Q4: Can this median be used to find other triangle properties?
A: Yes, knowing the median can help find the circumradius of the triangle, as the median equals the circumradius in a right triangle.
Q5: Is there a similar relationship for medians to other sides?
A: No, this specific relationship (median = half the side) only applies to the median drawn to the hypotenuse in a right triangle.