One of the legs of a right-angled triangle is 6. the other boat is 8. Find the length of the median drawn to the hypotenuse.

To solve the problem, we use the picture.
Let a right-angled triangle with legs AB = 6 cm and BC = 8 cm be given.
ВO is the median drawn to the hypotenuse.
Find the length of the hypotenuse using the Pythagorean theorem.
AC ^ 2 = AB ^ 2 + BC ^ 2 = 6 ^ 2 + 8 ^ 2 = 36 + 64 = 100.
AC = 10 cm.
Let us complete from triangle ABC a rectangle AВСD, in which ВD and AC are the diagonals of the rectangle, which at the point of their intersection are halved and equal to each other. Then
AC = ВD.
ВO = DO = AO = CO = (1/2) x AC = 10/2 = 5 cm.
Answer: The length of the median ВO = 5 cm.