Question

in a clock at 3 o' clock an hour hand and a minute hand makes right angle each other​

Answer 1

Answer:

Taking a quick look at the position of the clock hands between 2:00 and 3:00 shows that this 90 deg separation occurs between 2:25 and 2:30. Now, to figure it out…

We have to start at 2:00 when the minute hand is at 0 deg and the hour hand is at (360)*2/12 = 60 deg. We must find the time t it takes for the hour hand to move to an angle A(h) at the same time that the minute hand is at an angle of A(h) + 90.

The minute hand rotates at 360 deg per hour or (360 deg)/60 min = 6 deg/min (or 0.1 deg/sec).

The hour hand moves at 1/12th the speed of the second hand, so it’s rotational rate is 0.5 deg/min (or 0.0083 deg/sec).

So the angle A(m) of the minute hand [in degrees] at any time t [t in sec] will be A(m) = 0.1 t.

The angle of the hour hand will be A(h) = 60 + 0.0083 t. 60 deg was added because the hour hand, of course, has a “head start” of 60 deg at 2:00.

Now the task is to fine the time t at which A(m) = A(h) + 90 or

0.1 t = 60 + 0.0083 t + 90

This works out to t = 1635.8 s or 27.26 m or 27 min 15.6 sec

So…the hour and minute hands will form a right angle at 2:27m 15.6s

Step-by-step explanation:

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