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Find the degrees the angle between the hour hand and minute hand of a clock at Quarter past two 2:45 A.M.

Mathematics

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Answer

2π3 रेडियन\frac{2\pi}{3} \text{ रेडियन}

Step-by-step solution

3 steps

  1. घडीको मिनेट सुईले ६० मिनेटमा घुम्ने कोण पत्ता लगाउनुहोस्।

    मिनेट सुईले ६० मिनेटमा 360∘360^\circ वा 2π2\pi रेडियन घुम्छ।

  2. मिनेट सुईले १ मिनेटमा घुम्ने कोण पत्ता लगाउनुहोस्।

    १ मिनेटमा घुमेको कोण=2π रेडियन60 मिनेट=π30 रेडियन/मिनेट\text{१ मिनेटमा घुमेको कोण} = \frac{2\pi \text{ रेडियन}}{60 \text{ मिनेट}} = \frac{\pi}{30} \text{ रेडियन/मिनेट}

  3. मिनेट सुईले २० मिनेटमा घुम्ने कोण पत्ता लगाउनुहोस्।

    २० मिनेटमा घुमेको कोण=π30 रेडियन/मिनेट×20 मिनेट\text{२० मिनेटमा घुमेको कोण} = \frac{\pi}{30} \text{ रेडियन/मिनेट} \times 20 \text{ मिनेट} =20π30 रेडियन= \frac{20\pi}{30} \text{ रेडियन} =2π3 रेडियन= \frac{2\pi}{3} \text{ रेडियन}

    २० मिनेटमा मिनेट सुईले घुम्ने कोण 2π3 रेडियन\boxed{\frac{2\pi}{3} \text{ रेडियन}} हो।

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