Hello, GoldendoodleMom!
Find an algorithm for constructing a triangle given one side, $\displaystyle AB$,
and altitudes $\displaystyle h$ and $\displaystyle k$ from $\displaystyle A$ and $\displaystyle B$ respectively.
(Using straightedge-compass construction)
Draw line segment $\displaystyle AB.$
Locate its midpoint $\displaystyle M.$
Draw a semicircle with diameter $\displaystyle AB.$ Code:
* * *
* *
* *
* *
* *
A * - - - - * - - - - * B
M
With $\displaystyle A$ as center and radius $\displaystyle h$, swing an arc cutting the semicircle at $\displaystyle P.$
With $\displaystyle B$ as center and radius $\displaystyle k$, swing an arc cutting the semicircle at $\displaystyle Q.$
Code:
Q
∆ * * P
* ∆ o
* ∆ *
* o ∆ *
o ∆
* o ∆ *
A o - - - - * - - - - ∆ B
M
Draw $\displaystyle AQ$ and $\displaystyle BP$, extending them to meet at $\displaystyle C.$
The required triangle is $\displaystyle \Delta ABC.$