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This problem involves finding the length of side \( BC \) in a right triangle, where the following information is provided:

- Angle \( \angle A \) is \( 50^\circ \),
- Side \( AB = 3 \),
- We are solving for side \( BC \) (the side adjacent to the \( 50^\circ \) angle).

### Step 1: Identify the Trigonometric Ratio
Since we are given an angle and the adjacent side, and we need to find the opposite side \( BC \), we can use the tangent function:

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

Where:
- \( \theta = 50^\circ \),
- The opposite side is \( BC \),
- The adjacent side is \( AB = 3 \).

Thus, the equation becomes:

\[
\tan(50^\circ) = \frac{BC}{3}
\]

### Step 2: Solve for \( BC \)

\[
BC = 3 \times \tan(50^\circ)
\]

Using a calculator to find \( \tan(50^\circ) \):

\[
BC = 3 \times 1.1918 \approx 3.5754
\]

### Step 3: Round the Answer
We are asked to round the answer to the nearest hundredth:

\[
BC \approx 3.58
\]

Thus, the length of side \( BC \) is approximately **3.58**.

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

### Related Questions:
1. How would you solve for side \( AC \) in this triangle?
2. What would change if angle \( A \) was \( 60^\circ \) instead of \( 50^\circ \)?
3. How can you verify the result using another trigonometric function?
4. What is the Pythagorean theorem, and can it be used here?
5. How does rounding affect precision in trigonometric calculations?

### Tip:
Always ensure your calculator is set to degrees when working with angle measures in degrees!

Determine the length of BC in a right triangle where angle A is 50 degrees and side AB is 3. Round your answer to the nearest hundredth.

Learn how to find the length of side BC in a right triangle, given angle A is 50 degrees and side AB is 3. This problem involves the tangent function and trigonometric ratios. Suitable for students in Grades 9-12.

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