Hello, Joe!
The wording is rather clumsy . . .
Construct a triangle given: side $\displaystyle a,\;H_a$ (altitude to side $\displaystyle a$), $\displaystyle M_a$ (median to side $\displaystyle a$).
Draw a horizontal line $\displaystyle L.$
Erect a perpendicular to line $\displaystyle L$ and measure length $\displaystyle H_a$ to point $\displaystyle A.$ Code:
A
*


Ha 


L   *              
Using center $\displaystyle A$ and radius $\displaystyle M_a$, swing an arc cutting line $\displaystyle L$ at $\displaystyle D.$ Code:
A
*
\
 \
Ha  \ Ma
 \
 \
L   *   *  
D
$\displaystyle D$ is the midpoint of side $\displaystyle a.$
Using center $\displaystyle D$ and radius $\displaystyle \tfrac{1}{2}a$, swing arcs on both sides
. . cutting line $\displaystyle L$ at $\displaystyle B$ and $\displaystyle C.$ Code:
A
*
*\ *
*  \ *
*  \ *
*  \ *
*  \ *
* * * * * * * * *
B ½a D ½a C
And $\displaystyle ABC$ is our triangle!