Final answer:
To find the diagonal DB in trapezoid ABCD, apply the Pythagorean theorem to right triangle ADC, followed by trigonometric methods if required.
Step-by-step explanation:
The student's question involves finding the length of the diagonal DB in a trapezoid ABCD with given side lengths and angles. Although the provided information seems to mix vector analysis and geometric optics with trapezoid properties, to find the diagonal DB in the trapezoid, we need to focus solely on the geometry of the trapezoid and apply the Pythagorean theorem or other relevant geometric principles. Given m∠A=90° and AB ∥ CD, we can deduce that ADC is a right triangle with AD as one leg and DC as the hypotenuse. By the Pythagorean theorem, we can find the length of AC, and with AC and CB known, we can use trigonometric ratios to find the length of DB if necessary.