Question

Q.14 Find the angle between hour-hand and
minute-hand in a clock at
i) ten past eleven​

Answer 1

Answer:

The angle between hour-hand and  minute-hand in a clock at ten past eleven​ is 90°.

Step-by-step explanation:

Consider the provided information.

The time is time is 10 past eleven, which is 11:10 on the clock, it means the hour hand points at 11 and the minute hand points at 2 (The number 2 is 10 divisions  away from 12 that's why it represents 10 minutes).

The angle between two consecutive divisions of a clock is:

360°/12=30°

Now the number of division between 11 and 2 is 3, so multiply 30° with 3.

30°×3=90°

Hence, the angle between hour-hand and  minute-hand in a clock at ten past eleven​ is 90°.

Answer 2

The actual angle between hour-hand and  minute-hand in a clock at  ten past eleven​ is 85°.

Step-by-step explanation:

We have to find the angle between hour-hand and minute-hand in a clock at  ten past eleven.​

Firstly, the time 10 past eleven means the time in the clock is 11 : 10, that is the hour hand points at 11 and the minute hand points at 2(which represents 10 minutes).

Now, as we know that the angle between the two consecutive numbers on the clock is 30° and since there is a gap of three numbers between 11 and 2, so the angle between ten past eleven will be = 30° $\times$ 3 = 90°.

But this is the imaginary angle as at 11:10 we all know that the minute hand will be at fixed position or at 2 but the hour hand won't be fixed at or at 11 because if minute hand is moving 10 minutes then obviously hour hand will move some angle.

Also, the hour hand moves with the angle of 30° in one hour or 60 minutes.

So, in one minute the hour hand will move =  $\frac{30}{60} = \frac{1}{2}$ , which means in 10 minutes the minute hand will travel = $10 \times \frac{1}{2}$ = 5°.

Therefore, the actual angle between hour-hand and  minute-hand in a clock at  ten past eleven​ = 90° - 5° = 85°.