Final answer:
To find the length of side AB, we can use the Law of Cosines. Plugging the known lengths and angle into the formula, we can calculate the length of side AB to be approximately 16.96 cm.
Step-by-step explanation:
To find the length of side AB, we can use the Law of Cosines. This law relates the lengths of the sides of a triangle to the cosine of one of its angles. The formula is:
c^2 = a^2 + b^2 - 2abcos(C)
In this case, side AB is the side opposite the angle of 62 degrees. The known lengths are a = 12 cm and C = 62 degrees. Plugging these values into the formula, we get:
AB^2 = 12^2 + 12^2 - 2(12)(12)cos(62)
AB^2 = 144 + 144 - 288cos(62)
AB^2 ≈ 288.056
Taking the square root of both sides, we get:
AB ≈ 16.96 cm