Final answer:
The student can determine angle B in triangle ABC by subtracting the given angle A and the right angle from 180 degrees. However, without at least one side length, it's impossible to solve for the remaining sides using the Pythagorean theorem or trigonometric ratios.
Step-by-step explanation:
To solve for all the missing parts of a right triangle given one angle and using the Pythagorean theorem, we need two sides for a complete solution. However, with just one angle value given (88.6° for angle A), we can determine angle B since in right triangle ABC, the sum of angles is always 180°. Thus, angle B would be 180° - 90° - 88.6° = 1.4°. To find the lengths of sides a, b, and c, we would need at least one side length provided along with angle A to use trigonometric ratios or Pythagorean theorem.
The Pythagorean theorem is essential for solving the missing parts of right triangles when two side lengths are known. It is given by the formula a² + b² = c², which can be solved for the hypotenuse c as c = √(a² + b²). Without further information about the lengths of sides a or b, we cannot calculate the hypotenuse or the other side. In trigonometry, knowing an angle and a side in a right triangle allows us to calculate the other parts using the sine, cosine, and tangent functions.