What is the radian measure between the arms of watch at 5 pm
Answers
Answer:
5/6 π radians ; 2.618 radians
Explanation:
• A full circle is comprised of 2π radians.
• At 5 PM , the arms of a 12-hour clock are separated by 5/12 of a full circle.
• Thus the angle between them is 5/12 of 2π radians = 5/6 π radians or roughly 2.618 radians.
Given:
Time given = 5 pm
To find:
Angle measure in radian = ?
Step-wise solution:
Let us first understand the concept of radian:
The angle subtended by an arc of identical length as the radius at the centre of a circle is measured in radians.
First let us calculate angle in degrees at 5 pm:
At 6 pm angle = 180°
Angle at 5 pm = 180° - 30° (∵ The minute hand will be at 12 and hour hand at 5. We already know that the 12 sectors is divided at 30 ° equally)
∴ Angle at 5 pm = 150°
To calculate radian when angle is known use following formula:
Radians = Degrees × π / 180°
Radians = 150° × π / 180°
Radians = 150° × (3.14 / 180°). (∵π = 3.14)
Radians = 471 / 180
Radians = 2.61
Hence, 2.61 radians is the angle measure between the arms of watch at 5 pm.