Final answer:
Without specific dimensions or angles, it is not feasible to calculate the length of AD. The solution requires additional information to apply SOH CAH TOA, the Pythagorean theorem, or the cosine rule.
Step-by-step explanation:
The student's question requires the calculation of the length of the segment AD using trigonometric methods like SOH CAH TOA and the cosine rule, along with the Pythagorean theorem. Unfortunately, without a specific diagram or additional information such as lengths of sides or angles, it is not possible to provide a definitive answer. In general, to calculate a missing length in a triangle when using SOH CAH TOA, one would need at least one side length and an angle to find another side using sine, cosine, or tangent ratios. The Pythagorean theorem can be used in cases involving right-angled triangles to find a missing side if the other two sides are known.
When given a non-right-angled triangle, and the lengths of two sides and the included angle or the lengths of all three sides are known, the cosine rule can be applied to find the missing lengths. In these cases, if sides a and b and the angle C between them are known, side c can be found using c² = a² + b² - 2ab*cos(C).