https://file.aiquickdraw.com/mathbot/file/1725898250642rxs6ffi1.jpg

The image shows a right triangle with a 60° angle, a 90° angle, and the following dimensions:
- The hypotenuse is 11.
- One leg is marked as \( m \), and the other leg is given as \( 7\sqrt{3} \).

We can solve for \( m \) using trigonometric ratios. Since the triangle includes a 60° angle, we can apply the sine or cosine function for this:

- \( \sin(60^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{m}{11} \)

Given that \( \sin(60^\circ) = \frac{\sqrt{3}}{2} \), we substitute:

\[
\frac{\sqrt{3}}{2} = \frac{m}{11}
\]

Now, solve for \( m \):

\[
m = 11 \times \frac{\sqrt{3}}{2} = \frac{11\sqrt{3}}{2}
\]

Thus, \( m = \frac{11\sqrt{3}}{2} \).

Let me know if you'd like further clarification or more details!

### Related Questions:
1. How do you find the other side using trigonometry?
2. What if the triangle had a 45° angle instead?
3. Can you apply Pythagoras' theorem to verify this result?
4. What are the exact values for the sine and cosine of 30° and 60°?
5. How would you rationalize the denominator in this case?

### Tip:
When solving right triangles, remember that special triangles (like 30°-60°-90°) have known ratios, which can help simplify the process.

Solve for m. Do not convert your answer to decimal form. Rationalize the denominator and simplify your answer if necessary. The triangle has a 60° angle, a hypotenuse of 11, and a given leg of 7√3.

Learn how to solve for the unknown side in a right triangle with a 60° angle, hypotenuse of 11, and one known side. Apply trigonometric ratios and rationalize the denominator in this detailed step-by-step guide.

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