Question

Q7.find in degrees and radians the angle between the hour hand and minute hand of a clock at half past three

Answer 1

Here is the answer......

Answer 2

Answer:

The angle between the hour hand and minute hand at 3:30 = 75° =  $\frac{5\pi }{12}$ radians

Step-by-step explanation:

To find,

The angle between the hour hand and minute hand of a clock at half-past three in degrees and radians

Recall the concepts

180° = π radians

Solution:

We know that,

The hour hand makes one complete revolution in 12 hours

Angle covered by the hour hand in 12 hours = 360°

Angle covered by the hour hand in 1 hour = $\frac{360}{12}$ = 30°

The minute hand makes one complete revolution in 60minutes

Angle covered by the minute hand in 60 minutes  =360°

Angle covered by the minute hand in 1 minute = $\frac{360}{60}$ = 6°

Here, the time given is half past three

Half-past three = 3.30 = 3 hour 30 minutes = 3.5hours

Since the angle covered by the hour hand in hour = 30°

Angle covered by the hour hand in 3.5 hours = 3.5×30 = 105°

Since, the angle covered by the minute hand in 1 minute = 6°,

the angle covered by the minute hand in 30 minutes = 30× 6 = 180°

∴The angle between the hour hand and minute hand at 3.30 = 180° - 105° = 75°

To find the angle in radians

We have

180° = π radians

1° = $\frac{\pi }{180}$ radians

75° = $\frac{\pi }{180}X75$ radians

75° = $\frac{5\pi }{12}$ radians

∴The angle between the hour hand and minute hand at 3:30 = 75° =  $\frac{5\pi }{12}$ radians

#SPJ3