## Task 8 - 020828

Construct a right-angled triangle with the hypotenuse $A B=10 \mathrm{~cm}$! The foot of the altitude $h_{c}$ should divide the hypotenuse into two segments that are in the ratio $2: 3$.

Determine the length of $h_{c}$ from the construction! Describe the construction!
Draw the line segment $A B$. Divide it, for example, by the ray theorem construction, in the ratio $2: 3$. At the division point, erect the perpendicular, on which the height $h_{c}$ lies.

The other endpoint of the height is obtained according to Thales' theorem: the circle with $A B$ as diameter must be constructed. Its intersection with the erected perpendicular is the desired point $C$ of the triangle. This allows us to determine that the length of $h_{c} \approx 4.9 \text{~cm}$.