Discussion

When will be both hands of a clock at right angle, between 8pm and 9pm?

Answer: B

The hour hand moves \( 0.5^{\circ} \) a minute and the minute hand \( 6^{\circ} \), so at \( H \) hours \( M \) minutes the angle between them is

\[ \theta = \left| 30H - 5.5M \right| \]

With \( H = 8 \) and \( \theta = 90 \):

\[ \left| 240 - 5.5M \right| = 90 \]

\[ 5.5M = 150 \quad\Longrightarrow\quad M = \frac{300}{11} = 27\tfrac{3}{11} \]

The other root gives \( M = 60 \), which is 9 o'clock exactly and so outside the hour asked about.

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