Final answer:
The fencing required, we use the Law of Cosines to find the length of the third side of the triangular garden and then sum up all three sides to get the perimeter, rounding the result to the nearest meter.
Step-by-step explanation:
The student needs to calculate the fencing required for a triangular garden with two sides that are each 3.6 meters long and contain an angle of 80°.
To find the length of the third side, which will complete the perimeter, we can use the Law of Cosines:
c² = a² + b² - 2ab * cos(C),
where a and b are the lengths of the two equal sides, and C is the contained angle. Substituting the values:
c² = 3.6² + 3.6² - 2 * 3.6 * 3.6 * cos(80°),
c² = 12.96 + 12.96 - 25.92 * cos(80°),
After calculating the cosine of 80° and solving for c, we find the length of the third side. The perimeter of the triangular garden is the sum of all three sides. To find out how much fencing is needed, add the length of the third side to the length of the two equal sides (3.6 m + 3.6 m) and round to the nearest meter.