Type–3: Finding Angle Between Clock Hands (Angle / কোণ নিৰ্ণয়)

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Rule (নিয়ম): Angle (θ) = |30H − 11M/2|

• Where: H = Hour (ঘণ্টা), M = Minute (মিনিট), θ = Angle between the two hands (দুয়োটা কাঁটাৰ মাজৰ কোণ)

Important Values (গুৰুত্বপূর্ণ মান)

• Hour hand moves 30° per hour (ঘণ্টাৰ কাঁটা প্ৰতি ঘণ্টাত 30° আগবাঢ়ে।)


• Relative movement = 11/2° per minute.. (আপেক্ষিক গতি = 11/2° প্ৰতি মিনিট।)

Ex: Q. What is the angle between the two hands at 7:30 ? (প্ৰশ্ন: 7:30 বজাত দুয়োটা কাঁটাৰ মাজৰ কোণ কিমান ?)

Solⁿ (সমাধান)

• Here (ইয়াত), H = 7 and(ইয়াত) M = 30

• Apply the formula: θ = |30H − 11M/2|

θ = |30(7) − (11 × 30)/2|

θ = |210 − 165|

θ = 45°

Ans (উত্তৰ): Angle = 45°

7:30 বজাত দুয়োটা কাঁটাৰ মাজৰ কোণ = 45°

Main Points (গুৰুত্বপূর্ণ কথা)

• Use θ = |30H − 11M/2| to find the angle. (কোণ উলিয়াবলৈ θ = |30H − 11M/2| সূত্ৰ ব্যৱহাৰ কৰক।)


• Always take the positive value (absolute value).(সদায় ধনাত্মক মান (Absolute Value) লওক।)


• If asked for the smaller angle, the answer must be less than or equal to 180°. (সৰু কোণ বিচাৰিলে উত্তৰ 180° বা তাতকৈ কম হ’ব লাগিব।)

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Angle Between Hour and Minute Hands

Q. What is the angle between the hour and minute hands at 5:25 ?

Formula: Angle = ∣30H − 5.5M∣

Here, H = 5 and M = 25

               = ∣30(5) − 5.5(25)∣ = ∣150 − 137.5∣ = 12.5^∘

Ans: 12.5°

Trick:

At 5:25, the minute hand is at 150°, while the hour hand is at 162.5°.

162.5∘−150∘ = 12.5^∘

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Q. What is the angle between the hour and minute hands at 10:50 ?

Formula: Angle = ∣30H−5.5M∣|

Here, H = 10 and M = 50

=∣30(10) − 5.5(50)∣ = ∣300−275∣ = 25°

Ans: B) 25°

Trick:

At 10:50, the minute hand is at 300°.

The hour hand moves 50 minutes beyond 10: 50 × 0.5° = 25°

Hour hand position: 10 × 30° + 25° = 325°

Therefore: 325° − 300°= 25°

Ans: 25°