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!