Find the angle between minute hand and hour hand at 6 O’clock.
Last updated date: 26th Mar 2023
•
Total views: 216.5k
•
Views today: 2.93k
Answer
216.5k+ views
Hint: A clock has a shape of the circle made up of \[{{360}^{{}^\circ }}\], as a clock has 12 hours, each hour will draw an angle measure of \[{{30}^{{}^\circ }}\].
Our task is to find the angle between minute hand and hour hand at 6 O’clock.
These types of problems are called clock angle problems where we must find the angle between the hands of an analog clock at a specific time mentioned.
Generally, an analog clock that shows us time is divided into 12 sections, as there are 12 numbers on the clock that represents the hours.Keeping this in mind we can say that each number represents a definite angle.
As it is divided into 12 equal parts, the measure of the angle between each number is given as:
\[\dfrac{360}{12}=30\].
Thus, we can further say that, each hour will make an angle measure of \[{{30}^{{}^\circ }}\]in a clock.
Similarly, since there are 60 minutes in any clock, let us find out the angle measure by each minute.
The angle measure per minute is given as:
\[\dfrac{360}{60}=6\]
Therefore, it makes an angle measure of \[{{6}^{{}^\circ }}\] for every minute in the clock.
Now, we were supposed to find the angle made by the minute and hour hand at 6 O’clock.
So, when the time is 6 O’clock, we have six hours in between, where each hour makes an angle measure of \[{{30}^{{}^\circ }}\].
Therefore, we have:
\[\left( 6 \right)\left( 30 \right)=180\]
Therefore,\[{{180}^{{}^\circ }}\] is the angle made by the hour and minute hand of the clock at 6 O’clock.
Note: Alternatively, we can illustrate a diagram representing the time of 6 O’clock and observe that the minute hand and hour hand make a straight line, so we can directly say that the angle is \[{{180}^{{}^\circ }}\], since it is a straight line. \[{{180}^{{}^\circ }}\]angle is also called a straight angle.
Our task is to find the angle between minute hand and hour hand at 6 O’clock.
These types of problems are called clock angle problems where we must find the angle between the hands of an analog clock at a specific time mentioned.
Generally, an analog clock that shows us time is divided into 12 sections, as there are 12 numbers on the clock that represents the hours.Keeping this in mind we can say that each number represents a definite angle.
As it is divided into 12 equal parts, the measure of the angle between each number is given as:
\[\dfrac{360}{12}=30\].
Thus, we can further say that, each hour will make an angle measure of \[{{30}^{{}^\circ }}\]in a clock.
Similarly, since there are 60 minutes in any clock, let us find out the angle measure by each minute.
The angle measure per minute is given as:
\[\dfrac{360}{60}=6\]
Therefore, it makes an angle measure of \[{{6}^{{}^\circ }}\] for every minute in the clock.
Now, we were supposed to find the angle made by the minute and hour hand at 6 O’clock.
So, when the time is 6 O’clock, we have six hours in between, where each hour makes an angle measure of \[{{30}^{{}^\circ }}\].
Therefore, we have:
\[\left( 6 \right)\left( 30 \right)=180\]
Therefore,\[{{180}^{{}^\circ }}\] is the angle made by the hour and minute hand of the clock at 6 O’clock.
Note: Alternatively, we can illustrate a diagram representing the time of 6 O’clock and observe that the minute hand and hour hand make a straight line, so we can directly say that the angle is \[{{180}^{{}^\circ }}\], since it is a straight line. \[{{180}^{{}^\circ }}\]angle is also called a straight angle.

Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
