[Right triangle with an angle of ]

An acute angle of a right triangle is $30^{\circ}$, and the hypotenuse is 8.

Find the segments into which the altitude from the right angle vertex divides the hypotenuse.
Let $AB=8$ be the hypotenuse of the right triangle $ABC$, where $\angle A=30^{\circ}$, and $CD$ is the altitude. In

the right triangle $BCD$, the angle at vertex $B$ is $60^{\circ}$, so $\angle BCD=30^{\circ}, BD=\frac{1}{2}BC=\frac{1}{4}AB=2$.

## Answer

2 and 6.