At \( 3: 40 \) , the hour and minute hands of a clock are inclined at
1. Find the Angle in Degrees (°): The simplest way to find the angle is with the formula: Angle θ = | 30H - 5.5M |, where H is the hour and M is the minute.
- H = 3, M = 40
- θ = | 30(3) - 5.5(40) |
- θ = | 90 - 220 | = |-130| = 130°.
2. Convert Degrees to Radians: - To convert from degrees to radians, we use the conversion factor: Radians = Degrees × (π / 180).
- Radians = 130 × (π / 180)
- Radians = 130π / 180
- Simplifying the fraction by dividing the top and bottom by 10 gives: 13π/18.
Final Answer: The angle between the hands at 3:40 is 13π/18 radians.
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