Answer
Verified
333.8k+ 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
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Write an application to the principal requesting five class 10 english CBSE
Difference Between Plant Cell and Animal Cell
a Tabulate the differences in the characteristics of class 12 chemistry CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
Discuss what these phrases mean to you A a yellow wood class 9 english CBSE
List some examples of Rabi and Kharif crops class 8 biology CBSE