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We are tasked with finding the length of the hypotenuse in the given right-angled triangle, where the angle opposite the 8-meter side is \( 60^\circ \).

### Step-by-Step Solution:

1. **Given Information:**
   - Angle \( \theta = 60^\circ \)
   - Adjacent side to \( \theta = 8 \) meters (horizontal side)
   - We need to find the hypotenuse.

2. **Trigonometric Function to Use:**
   Since we know the angle and the adjacent side, we can use the **cosine** function:
   \[
   \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
   \]
   Plugging in the known values:
   \[
   \cos(60^\circ) = \frac{8}{\text{hypotenuse}}
   \]

3. **Value of \( \cos(60^\circ) \):**
   \[
   \cos(60^\circ) = 0.5
   \]

4. **Solving for the Hypotenuse:**
   \[
   0.5 = \frac{8}{\text{hypotenuse}}
   \]
   Multiply both sides by the hypotenuse:
   \[
   \text{hypotenuse} = \frac{8}{0.5} = 16 \, \text{meters}
   \]

### Final Answer:
The length of the hypotenuse is \( 16 \, \text{meters} \).

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Would you like more details or have any further questions? Here are some related questions to explore:

1. How would you solve for the opposite side in this triangle?
2. What is the formula for finding the hypotenuse using the sine function instead?
3. How would the solution change if the angle were different, say \( 30^\circ \)?
4. What are the other trigonometric ratios in this triangle (sine and tangent)?
5. Can we use the Pythagorean theorem here if the opposite side is known?

**Tip:** In right-angled triangles, always identify which sides correspond to the given angle to choose the correct trigonometric ratio (sine, cosine, or tangent).

Find the length of the hypotenuse in the right-angled triangle with a 60° angle and adjacent side length of 8 meters.

Learn how to find the hypotenuse of a right-angled triangle with a 60° angle and an adjacent side of 8 meters. This problem uses the cosine function and is suitable for students in Grades 8-10.

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