To solve for side $BC$ in the right triangle where $\angle A = 90^\circ$, $\angle D = 50^\circ$, and side $AD = 17.0$ meters, we can use trigonometric ratios.

Since we know:

• $AD$ (adjacent side to $\angle D$) = 17.0 meters,
• $\angle D = 50^\circ$,
• and we need to find $BC$ (the opposite side to $\angle D$),

we can use the tangent function:

$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Substitute the known values:

$\tan(50^\circ) = \frac{BC}{AD}$

$\tan(50^\circ) = \frac{BC}{17.0}$

Now solve for $BC$:

$BC = 17.0 \times \tan(50^\circ)$

Using a calculator:

$\tan(50^\circ) \approx 1.1918$

$BC \approx 17.0 \times 1.1918 \approx 20.2606 \, \text{meters}$

This doesn't match the expected result of 15.5m. It seems there might be an additional piece of information missing or a slight misinterpretation in the triangle description, based on the image.

Could you clarify the triangle or let me know if there's another angle or side that could help refine the calculation?

Meanwhile, here are some follow-up questions to expand the topic:

1. How would the calculation change if you used the sine or cosine function instead of tangent?
2. What is the importance of the Pythagorean theorem in solving for unknown sides in right triangles?
3. If the given triangle had a different angle, how would it affect the length of $BC$?
4. How can you verify the result using another method, such as the sine or cosine rule?
5. Can you find side $AB$ after finding $BC$ using the same trigonometric principles?

Tip: Always double-check your angle measures and ensure your calculator is in the correct mode (degrees/radians) for the problem at hand.