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find Y. Once you get the correct answer round to the nearest tenth

The problem involves a right triangle where we are tasked to solve for \( y \), rounding to the nearest tenth. Let's break it down.

### Given:
- The hypotenuse is \( 350 \, \text{ft} \).
- The angle opposite \( y \) is \( 28^\circ \).
- We want to find \( y \) (the length of the side adjacent to the angle \( 28^\circ \)).

### Using Trigonometry:
In a right triangle, the cosine of an angle is defined as:
\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

Here:
\[
\cos(28^\circ) = \frac{y}{350}
\]

### Solving for \( y \):
Rearranging the equation:
\[
y = 350 \cdot \cos(28^\circ)
\]

### Calculating \( y \):
Using a calculator:
\[
\cos(28^\circ) \approx 0.8829
\]
\[
y = 350 \cdot 0.8829 \approx 309.0
\]

### Final Answer:
\[
y = 309.0 \, \text{ft}
\]

Let me know if you'd like to see a step-by-step breakdown of the calculations or additional trigonometry concepts!

---

### Related Questions:
1. What is the value of \( x \) (the opposite side)?
2. How would you find the angle if the hypotenuse and \( y \) were given instead?
3. Can you calculate the area of this triangle using the values of \( x \) and \( y \)?
4. What trigonometric function would you use if \( x \) was given instead of \( y \)?
5. How can you use the Pythagorean theorem to verify your results?

### Tip:
When solving trigonometric problems, make sure your calculator is set to the correct mode (degrees vs radians) based on the angle measurement provided!

Learn how to solve for y in a right triangle using trigonometric ratios. Given a hypotenuse of 350 ft and an angle of 28°, this problem demonstrates how to use the cosine function to find the adjacent side, rounded to the nearest tenth.

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