The question is asking for the length of the side $BC$ of the roof truss using Pythagoras' theorem.

From the diagram:

1. $AB = 5.5 \, \text{m}$ (one side of the triangle),
2. $BD = 4 \, \text{m}$ (vertical height),
3. $DC = 5 \, \text{m}$ (horizontal length).

The triangle $\triangle BDC$ is a right triangle where $BC$ is the hypotenuse. Using Pythagoras' theorem:

$BC^2 = BD^2 + DC^2$

Calculation:

$BC^2 = 4^2 + 5^2$ $BC^2 = 16 + 25$ $BC^2 = 41$

Taking the square root: $BC = \sqrt{41} \approx 6.4 \, \text{m}$

Final Answer:

The length of $BC$ is approximately 6.4 meters.

Would you like a more detailed breakdown or further help?

Here are some related questions to expand on this:

1. How would you calculate the area of $\triangle ABC$ using the given dimensions?
2. Can you calculate the angles of $\triangle BDC$ using trigonometric ratios?
3. What other methods could verify the length of $BC$?
4. What is the total perimeter of $\triangle ABC$?
5. How would you find the height from $A$ to $BC$?

Tip: When working with triangles, double-check which side is the hypotenuse before applying the Pythagorean theorem!