At what time between 2:00 and 3:00 will the hands of a clock be at right angles?

₹0.0

Question: At what time between 2:00 and 3:00 will the hands of a clock be at right angles?

Options:

Correct Answer: 2:45

Solution:

The hands of a clock are at right angles at approximately 2:45.

At what time between 2:00 and 3:00 will the hands of a clock be at right angles?

At what time between 2:00 and 3:00 will the hands of a clock be at right angles?

Step 1: Understand that a clock has two hands: the hour hand and the minute hand.
Step 2: Know that the hour hand moves 30 degrees for each hour (360 degrees / 12 hours).
Step 3: Calculate the position of the hour hand at 2:00. It is at 60 degrees (2 hours * 30 degrees).
Step 4: The minute hand moves 6 degrees for each minute (360 degrees / 60 minutes).
Step 5: Set up the equation for when the hands are at right angles (90 degrees apart).
Step 6: The position of the minute hand after 'm' minutes is 6m degrees.
Step 7: The position of the hour hand after 'm' minutes is 60 + 0.5m degrees (since it moves 0.5 degrees per minute).
Step 8: Set up the equation: |(60 + 0.5m) - (6m)| = 90.
Step 9: Solve the equation for 'm' to find the minutes when the hands are at right angles.
Step 10: You will find two solutions, one of which is approximately 45 minutes past 2:00.

Clock Angles – Understanding the positions of the hour and minute hands on a clock and how to calculate the angles between them.
Time Calculation – Calculating specific times based on the movement of clock hands and their relative positions.