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We are dealing with a right triangle, where:

- \( y \) is the side opposite to the \( 27^\circ \) angle,
- \( 350 \, \text{ft} \) is the adjacent side (base of the triangle),
- \( x \) is the hypotenuse, and
- We need to find \( y \), rounding the answer to the nearest tenth.

We can use the trigonometric function tangent (\( \tan \)) to solve for \( y \), because:

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

For this triangle:

\[
\tan(27^\circ) = \frac{y}{350}
\]

Now, solving for \( y \):

\[
y = 350 \times \tan(27^\circ)
\]

Let me calculate that for you.

\[
y \approx 350 \times 0.5095 \approx 178.3 \, \text{ft}
\]

Thus, the value of \( y \) is approximately **178.3 feet**.

Would you like more details or have any questions?

### Related Questions:
1. How can you use sine or cosine to find the hypotenuse \( x \)?
2. What are the properties of a right triangle that make trigonometric ratios possible?
3. How does rounding affect accuracy in real-world problems involving measurements?
4. What is the difference between the adjacent, opposite, and hypotenuse in a right triangle?
5. How can inverse trigonometric functions be used to find angles?

### Tip:
Always make sure your calculator is set to degrees (not radians) when working with angle measures in degrees!

Find y. Round to the nearest tenth: A right triangle with an angle of 27 degrees, an adjacent side measuring 350 ft, and an unknown opposite side y.

Learn how to find the length of the opposite side in a right triangle using the tangent function. Given an angle of 27 degrees and an adjacent side of 350 ft, calculate the length of y, rounded to the nearest tenth. Suitable for high school students.

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