Answer
77.7k+ views
Hint: The given problem is from basic introduction to angles. The degree measurement has a relation with radian measurement of angle. So here first we convert 1’’ in degree form and then calculate its radian form.
Complete step by step solution:
As we know that the angle can be measured in degree as well as radian. There will be a relation for conversion of degree form into radian form that is given by
π radian = 180°
or
1° = π/180 radian
We can divide 1° angle into 60’ (minutes) then the 1’ (minute) can also be divided into 60’’ (seconds).
1° = 60’
1’ = 60’’
So according to degree and radian relation we can write 1° as
$60' = \dfrac{\pi }{{180}}rad$
So, the value of 1’ in radian would be
$1' = \dfrac{\pi }{{180 \times 60}}rad$
1’ (minute) is equal to 60’’ (seconds).
So the relation can be written as
$60'' = \dfrac{\pi }{{180 \times 60}}rad$
The value of 1’’ will be
$1'' = \dfrac{\pi }{{180 \times 60 \times 60}}rad \\
1'' = \dfrac{\pi }{{648000}}radian \\ $
This is the required solution for a given problem.
In geometry, an angle can be defined as the figure formed by two rays meeting at a common endpoint. An angle can be measured in degree and radian. One radian is the angle made at the center of a circle by an arc whose length is equal to the radius of the circle.
Note: Degree is a measure of an angle. One degree is one 360th part of a full circle. Each degree is divided into minutes and seconds. The degree is divided into 60 minutes. The minute is divided again into 60 seconds for fine measurements.
Complete step by step solution:
As we know that the angle can be measured in degree as well as radian. There will be a relation for conversion of degree form into radian form that is given by
π radian = 180°
or
1° = π/180 radian
We can divide 1° angle into 60’ (minutes) then the 1’ (minute) can also be divided into 60’’ (seconds).
1° = 60’
1’ = 60’’
So according to degree and radian relation we can write 1° as
$60' = \dfrac{\pi }{{180}}rad$
So, the value of 1’ in radian would be
$1' = \dfrac{\pi }{{180 \times 60}}rad$
1’ (minute) is equal to 60’’ (seconds).
So the relation can be written as
$60'' = \dfrac{\pi }{{180 \times 60}}rad$
The value of 1’’ will be
$1'' = \dfrac{\pi }{{180 \times 60 \times 60}}rad \\
1'' = \dfrac{\pi }{{648000}}radian \\ $
This is the required solution for a given problem.
In geometry, an angle can be defined as the figure formed by two rays meeting at a common endpoint. An angle can be measured in degree and radian. One radian is the angle made at the center of a circle by an arc whose length is equal to the radius of the circle.
Note: Degree is a measure of an angle. One degree is one 360th part of a full circle. Each degree is divided into minutes and seconds. The degree is divided into 60 minutes. The minute is divided again into 60 seconds for fine measurements.
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