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Find the height of a right triangle dropped to the hypotenuse, given that the base of this height divides the hypotenuse into segments of 1 and 4.

#
Let $A B C$ be a right triangle with hypotenuse $A B$, and $C H$ be its altitude, $B H=1, A H=4$.

According to the altitude theorem of a right triangle drawn from the vertex of the right angle,

$$
C H^2=B H \cdot A H=1 \cdot 4=4
$$

Therefore, $C H=2$.

## Answer

2.