https://file.aiquickdraw.com/mathbot/file/1725909958457p4bfdjl5.jpg

The triangle shown in the image is a 30°-60°-90° right triangle, which has special properties. In such a triangle:

- The side opposite the 30° angle is half the length of the hypotenuse.
- The side opposite the 60° angle is \( \sqrt{3} \) times the length of the side opposite the 30° angle.

In this case:
- The hypotenuse (the side opposite the right angle) is 15 yards.
- You are asked to find \( y \), which is the side opposite the 60° angle.

Using the known properties of a 30°-60°-90° triangle:
1. The side opposite the 30° angle (the shorter leg) is half of the hypotenuse, so:
   \[
   \text{Shorter leg} = \frac{15}{2} = 7.5 \text{ yards}
   \]
2. The side opposite the 60° angle (the longer leg, which is \( y \)) is:
   \[
   y = 7.5 \times \sqrt{3}
   \]

So, the exact value of \( y \) in simplest radical form is:
\[
y = \frac{15\sqrt{3}}{2} \text{ yards}
\]

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

Here are 5 related questions to expand your understanding:
1. How do the side ratios of a 30°-60°-90° triangle differ from other right triangles?
2. What are some practical applications of the 30°-60°-90° triangle in real-world problems?
3. How can we convert the radical form \( \frac{15\sqrt{3}}{2} \) into a decimal approximation?
4. What is the relationship between the angles and side lengths in other special right triangles like the 45°-45°-90° triangle?
5. How would you find the area of this triangle?

**Tip:** Whenever you encounter a 30°-60°-90° triangle, remember the ratio of the sides is always 1: \( \sqrt{3} \): 2.

Find y in a 30°-60°-90° triangle with the hypotenuse of 15 yards. Write the answer in simplest radical form.

Learn how to solve for the side opposite the 60° angle in a 30°-60°-90° triangle. The hypotenuse is given as 15 yards. This problem uses the properties of special right triangles and provides a solution in simplest radical form. Suitable for students in Grades 8-10.

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