8,9

The median to the hypotenuse of a right triangle is equal to $m$ and divides the right angle in the ratio 1:2. Find the sides of the triangle.
Let $C M$ be the median of the right triangle $A B C$ ( $\angle C=90^{\circ}$ ). Then $C M=A M=B M=m, A B=2 m$. If $\angle B C M>\angle A C M$, then $\angle B C M=60^{\circ}, \angle A C M=30^{\circ}$. Therefore, $\angle A=30^{\circ}$.

![](https://cdn.mathpix.com/cropped/2024_05_06_0ef0b80dacb6d98eff5ag-24.jpg?height=335&width=732&top_left_y=1279&top_left_x=663)

Answer

$2 m, m, m \sqrt{3}$.

Submit a comment