Final answer:
Without specific details about the triangle or angles involved, we cannot give the exact measure of angle CBD or lengths of segments CD, BC, and BD. To find these measurements, one would typically use trigonometric ratios and principles like the Pythagorean theorem.
Step-by-step explanation:
To determine the measure of angle CBD, the length of segment CD, the appropriate trigonometric ratio for comparing BC to CD, and the approximate lengths of BC and BD, we need specific information about the triangle and angles in question, which is not provided in your message. We often use basic trigonometry to find these measurements in right-angled triangles. The Pythagorean theorem can be used to find lengths of sides, and trigonometric ratios such as sine, cosine, and tangent are used to relate angles to side lengths.
For example, if angle CBD is known and we also know the length of one side adjacent to the angle (like BC), we could use the cosine ratio to find the length of the other side (CD). Conversely, if we know the opposite side (CD) and the hypotenuse (BD), we would use the sine ratio. Without additional information on the triangle's sides or angles, it is impossible to provide the exact measurements you are asking for.