Using the Pythagorean Theorem and trigonometric functions, we find that the length of side AB is 8.1 centimeters.
We know that AC is the hypotenuse of the triangle, and that AB and BC are the other two sides. We also know that the length of AC is 12 centimeters.
Substituting these values into the Pythagorean Theorem, we get:
AC^2 = AB^2 + BC^2
12^2 = AB^2 + BC^2
We can solve for AB by squaring both sides of the equation and then taking the square root of both sides:
AB^2 = 12^2 - BC^2
AB = sqrt(12^2 - BC^2)
We don't know the length of BC, but we can use the fact that the triangle is a right triangle to find it. We know that the sum of the angles in a triangle is 180 degrees, so we can write the following equation:
62° + angle B + angle C = 180°
Subtracting 62° from both sides, we get:
angle B + angle C = 118°
We also know that the angles in a right triangle sum to 90 degrees, so we can write the following equation:
angle B + angle C = 90°
Setting these two equations equal to each other, we get:
90° = 118° - angle B
angle B = 118° - 90°
angle B = 28°
Now that we know the value of angle B, we can use the trigonometric function sine to find the length of BC. Sine is defined as the opposite side over the hypotenuse, so we can write the following equation:
sin(28°) = BC / 12
Multiplying both sides by 12, we get:
BC = 12 * sin(28°)
BC = 6.4 centimeters
Now that we know the length of BC, we can substitute it into the equation we found for AB:
AB = sqrt(12^2 - BC^2)
AB = sqrt(12^2 - 6.4^2)
AB = 8.1 centimeters
Therefore, the length of side AB is 8.1 centimeters.