In a right-angled triangle, one of the angles 45 is hypotenuse 16. find the median drawn to the hypotenuse.

Since in a right-angled triangle one of the acute angles is 45, the second acute angle is also equal to (90 – 45) = 45, and therefore the ABC triangle is right-angled and isosceles.

AB = BC.

The median BM, in an isosceles triangle, also has a height and a bisector, then AM = CM = AC / 2 = 16/2 = 8 cm, angle ABM = 90/2 = 450, angle AMB = 90.

Then the triangle ABM is rectangular and isosceles, BM = AM = 8 cm.

Answer: The median length is 8 cm.