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To solve the problem, we need to calculate the perimeter of the right-angled triangle using trigonometry. The triangle has a known angle (43°) and one side (13.8 m), which is the adjacent side to the angle.

### Step-by-step solution:

1. **Label the triangle**:
   - Let \( A = 43^\circ \) (the given angle).
   - The adjacent side is 13.8 m.
   - We need to find the opposite side (\( O \)) and the hypotenuse (\( H \)).

2. **Find the opposite side** using the tangent function:
   \[
   \tan(A) = \frac{O}{\text{adjacent}}
   \]
   \[
   \tan(43^\circ) = \frac{O}{13.8}
   \]
   \[
   O = 13.8 \times \tan(43^\circ)
   \]

3. **Find the hypotenuse** using the cosine function:
   \[
   \cos(A) = \frac{\text{adjacent}}{H}
   \]
   \[
   \cos(43^\circ) = \frac{13.8}{H}
   \]
   \[
   H = \frac{13.8}{\cos(43^\circ)}
   \]

4. **Calculate the perimeter**:
   The perimeter is the sum of all sides of the triangle:
   \[
   \text{Perimeter} = O + \text{adjacent} + H
   \]

Let me calculate this for you.The perimeter of the right-angled triangle is approximately **45.5 meters**, rounded to 1 decimal place.

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

Here are some related questions:
1. How do you calculate the area of this triangle?
2. Can you explain why trigonometric functions were used here?
3. How would you find the missing angle of the triangle?
4. What is the relationship between sine, cosine, and tangent in a right-angled triangle?
5. How can Pythagoras' theorem be used to check the solution?

**Tip:** Always ensure your calculator is set to the correct mode (degrees or radians) when working with angles in trigonometric functions.

Using trigonometry, work out the perimeter of the right-angled triangle with one angle of 43 degrees and the adjacent side of 13.8 meters. Give your answer in meters to 1 decimal place.

Learn how to calculate the perimeter of a right-angled triangle with one angle of 43° and an adjacent side of 13.8 meters using trigonometry. The problem involves using the tangent and cosine functions to find the unknown sides, suitable for students in Grades 9-12.

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