To solve for the length of side BC in the given triangle, let's analyze the problem and proceed step-by-step.

Given:

1. Triangle ABD is divided into two right triangles, $\triangle ABC$ and $\triangle ADC$, where $C$ is the midpoint on $BD$.
2. AD = 17.0 , m.
3. Angle $\angle ABC = 50^\circ$.
4. $\angle BCA$ is $90^\circ$ (right triangle property).

We aim to calculate the length of BC.

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Steps to Solve:

Since $\triangle ABC$ is a right triangle:

1. Use the sine function since we are given the angle $\angle ABC$ and the hypotenuse $AD = 17.0 \, m$.

$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

Here:

• $\theta = 50^\circ$,
• Opposite side to $\theta$ is BC,
• Hypotenuse is $AD = 17.0 \, m$.

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

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Calculation:

1. Find $\sin(50^\circ)$ using a calculator:

$\sin(50^\circ) \approx 0.766$

2. Substitute into the equation:

$0.766 = \frac{BC}{17.0}$

3. Solve for $BC$:

$BC = 17.0 \times 0.766$

$BC \approx 13.02 \, \text{m}$

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Final Answer:

The length of side $BC$ is approximately 13.0 meters.

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Would you like further clarification or help with a similar problem?

Here are 5 related questions you might find useful:

1. How do we solve for $BD$ in this triangle?
2. How can we find $CD$ using trigonometry?
3. What if we are given another angle? How would the solution change?
4. How do we use the cosine rule to solve triangles without a right angle?
5. How do you solve for the area of triangle $ABD$?

Tip: For right triangles, always identify the hypotenuse, adjacent, and opposite sides relative to the given angle before selecting the appropriate trigonometric function.