1. **Problem Statement:** Determine the length of cylinder CB in the given mechanical diagram where angles are 90°, 25°, and 55°. 2. **Understanding the problem:** The points A, C, and B form a triangle with angles 90° at B, 25° adjacent to CB, and 55° near A. We want to find the length of segment CB. 3. **Relevant formula:** In a right triangle, the lengths of sides relate to angles via trigonometric functions. Since angle B is 90°, triangle ACB is right-angled at B. 4. **Step-by-step solution:** - Since angle B is 90°, angles A and C must be 55° and 35° respectively (because 180° - 90° = 90°, and 25° + 55° = 80°, so the 25° angle is adjacent to CB, so the 25° is part of the geometry but the triangle angles are 90°, 55°, and 35°). - Assuming the length AC is known or can be used as a reference, we can use the sine or cosine rules to find CB. - Using the sine rule: $$\frac{CB}{\sin 55^\circ} = \frac{AC}{\sin 90^\circ}$$ - Since $\sin 90^\circ = 1$, then $$CB = AC \times \sin 55^\circ$$ 5. **Explanation:** The sine of an angle in a right triangle gives the ratio of the opposite side to the hypotenuse. Here, CB is opposite to angle 55°, and AC is the hypotenuse. 6. **Final answer:** The length of cylinder CB is $$CB = AC \times \sin 55^\circ$$ Without the length of AC given, this is the expression for CB.