
Find in degrees and radians the angle between the hour hand and minute hand of a clock at half past three.
Answer
523.5k+ views
2 likes
Hint: Find the time from the given statement. First find the angle made by the hour hand from at half past three. Then find the angle made by the minute’s hand, now subtract these angles to get the angle made by both hour and minute hand in degree. Convert it to radians by multiplying the angle with .
Complete step-by-step answer:
We have to find the angle between the hour hand and minute hand of a clock. We have been given the time as half past three, which means that it is 30 minutes past the hour i.e., it is 30 minutes past . Hence the time is which is half past three.
We know that a clock is in a circle. Total angle of the circle is or .
A clock has a total of 12 hours shown in it. Thus we can write that, .
Now let us find the angle made by the clock in 1 hour.
Similarly, we know that . Hence we can change the above expression as,
.
Thus for 60 min it is , so for 1 minute it will be,
Now we found the time as . Here the hour hand travels 3 hours and 30 minutes from at half past three.
Thus, the hour hand travels= 3 hours and 30 minutes
We found out that, and , thus substitute these values and simplify it.
Thus the total angle made by the hour hand= .
Similarly let us find the angle made by the minute’s hand.
Now again we know that,
Thus for the angle is,
Hence in 30 minutes the angle is,
Thus the angle between the hour hand the minute hand at half past three= (angle made by the minutes hand) – (angle made by the hour hand)=
Thus we got the angle between the hour hand and minutes hands as , which is in degrees.
Now let us convert the given angle of degrees to radians. To convert degrees to radians, multiply the angle with . Let us consider the angle as equal to . Hence, . Now let us convert it to radians.
Thus we the angle between the hour hand and minute hand as,
In degrees, .
In radians, .
Thus we got the required values.
Note: The basic of questions like these is that you should know the conversion of the hour and minutes Hand with respect to the angle subtended by the clock. Remember the basics of conversion from hours to minutes. Also keep in mind that the total angle subtended by the clock is or , which is the same as in a circle.
Complete step-by-step answer:
We have to find the angle between the hour hand and minute hand of a clock. We have been given the time as half past three, which means that it is 30 minutes past the hour i.e., it is 30 minutes past
We know that a clock is in a circle. Total angle of the circle is
A clock has a total of 12 hours shown in it. Thus we can write that,
Now let us find the angle made by the clock in 1 hour.
Similarly, we know that
Thus for 60 min it is
Now we found the time as
Thus, the hour hand travels= 3 hours and 30 minutes
We found out that,
Thus the total angle made by the hour hand=
Similarly let us find the angle made by the minute’s hand.
Now again we know that,
Thus for
Hence in 30 minutes the angle is,
Thus the angle between the hour hand the minute hand at half past three= (angle made by the minutes hand) – (angle made by the hour hand)=
Thus we got the angle between the hour hand and minutes hands as
Now let us convert the given angle of degrees to radians. To convert degrees to radians, multiply the angle with
Thus we the angle between the hour hand and minute hand as,
In degrees,
In radians,
Thus we got the required values.
Note: The basic of questions like these is that you should know the conversion of the hour and minutes Hand with respect to the angle subtended by the clock. Remember the basics of conversion from hours to minutes. Also keep in mind that the total angle subtended by the clock is
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
School Full course for CBSE students
₹41,848 per year
Recently Updated Pages
Master Class 10 Computer Science: Engaging Questions & Answers for Success

Master Class 10 Maths: Engaging Questions & Answers for Success

Master Class 10 English: Engaging Questions & Answers for Success

Master Class 10 General Knowledge: Engaging Questions & Answers for Success

Master Class 10 Science: Engaging Questions & Answers for Success

Master Class 10 Social Science: Engaging Questions & Answers for Success

Trending doubts
What is the past participle of wear Is it worn or class 10 english CBSE

What is Whales collective noun class 10 english CBSE

What is potential and actual resources

For what value of k is 3 a zero of the polynomial class 10 maths CBSE

What is the full form of POSCO class 10 social science CBSE

Which three causes led to the subsistence crisis in class 10 social science CBSE
