To find the height $h$ in this trapezoidal figure, we can break down the problem as follows.

1. Identifying Key Components:

   • $AB$ and $CD$ are the non-parallel sides.
   • $BC$ is the height $h$.
   • $AD$ is the base of the trapezoid.
   • Angle $\angle ADB = 24^\circ$ and angle $\angle ABC = 20^\circ$.
   • $BD = 300 \text{ units}$ and $AB = 300 \cdot x$.

2. Using Trigonometry:

   • From point $B$, we can drop a perpendicular to side $AD$ and label the point where the height meets $AD$ as $P$. Thus, we can treat triangle $ABP$ and $BPC$ as right triangles.

3. For triangle $ABD$:

   • Use the tangent function based on angle $24^\circ$. $\tan(24^\circ) = \frac{h}{300}$ Solving for $h$, we get: $h = 300 \cdot \tan(24^\circ)$ Using a calculator, $\tan(24^\circ) \approx 0.4452$.

   Therefore: $h = 300 \cdot 0.4452 = 133.56 \text{ units}.$

Hence, the height $h$ is approximately 133.56 units.

Would you like more details, or do you have any questions?

Here are five related questions to expand on the topic:

1. How would you find the area of this trapezoid?
2. Can we calculate the length of the unknown side $AB$?
3. How does the tangent function help in solving right triangles?
4. What would happen if the angles or side lengths changed?
5. How does knowing the height affect the area and other properties of the trapezoid?

Tip: Trigonometric functions like sine, cosine, and tangent are powerful tools for solving right triangle problems, especially when angles and side lengths are involved.