This triangle can be solved using trigonometric principles because it includes a 60° angle and side lengths.

Step-by-Step Solution:

1. Identify the triangle's sides relative to the angle:

   • The side opposite the 60° angle is 9.
   • The side adjacent to the 60° angle is 8.
   • The hypotenuse is $x$.

2. Use the Pythagorean Theorem (if necessary): Since two sides of the right triangle are given, we can compute the hypotenuse: $x = \sqrt{9^2 + 8^2}$ $x = \sqrt{81 + 64} = \sqrt{145}$ $x \approx 12.04$

3. Verify with trigonometric ratios (optional): For the given 60° angle, using the sine function: $\sin(60^\circ) = \frac{\text{opposite}}{\text{hypotenuse}}$ $\sin(60^\circ) = \frac{9}{x}$ $x = \frac{9}{\sin(60^\circ)}$ Since $\sin(60^\circ) = \frac{\sqrt{3}}{2} \approx 0.866$: $x = \frac{9}{0.866} \approx 12.04$

Thus, the hypotenuse $x \approx 12.04$.

Would you like further clarifications or additional calculations?

Here are some related questions you might explore:

1. How do you calculate angles in a triangle if all sides are known?
2. How does cosine differ from sine in right triangle trigonometry?
3. Can the law of sines apply to this triangle? Why or why not?
4. How is the value of $\sin(60^\circ)$ derived from geometry?
5. What is the importance of the Pythagorean theorem in trigonometry?

Tip: Always double-check your trigonometric ratios and values for common angles like 30°, 45°, and 60°!