Question

Find tha degrees and radians tha angle between tha minute hand of a clock and tha hour hand when tha time is 7.20 a.m

Answer 1

Hi !!!

This is your answer.

We have to calculate the degree and radian covered by the minute hands and hour hand of a clock when it is 7:20 am.

Two points to remember.....

Angle at every interval one minute is 6°.
It is because a hand makes a complete angle during its full revolution of 60 minutes. So, in 60 minutes it covers 360°. So, in one minute it covers 360°/60° = 6°.
Second point - The difference between the two hands (i. e. minute and hour hand) will not be of 20 minutes.
It is because.......
We know that after every interval of 12 minutes, the hour hand of the moves by 6°. As the time is 7:20 am, so we can say that the hour hand will cover 2 minutes or 12°.

Hence, the difference of hour hand and minute hand will be of (20 - 2) minutes = 18 minutes or 18 × 6 degrees.

Calculation :-

Degree between two hands when the time is 7:20 = (20 -2) × 6
= 18× 6 = 108°.

Now, moving to the calculation of radian....

We know that..
$radian \: = \frac{\pi}{180} \times degrees \\ = \frac{\pi}{180} \times 108$
$= \frac{\pi}{180} \times 108 \\ = \frac{\pi}{45} \times 27 \\ = \frac{\pi}{5} \times 3 \\ = \frac{3\pi}{5}$
Hence,radian is 3π/5 or 1.88.

Hope you got the answer.......