Question

The radian measure of the angle between the minute hand of a clock and the hour hand at 12:30 is

Answer 1

Tᴏ Fɪɴᴅ :-

• The radian measure of the angle between the minute hand of a clock and the hour hand at 12:30 is ?

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :-

• Angle b/w Minute hand & Hour Hand in Degree is :- [ 30*Hour - Minutes*(11/2) ]
• 180° = π Radian

Sᴏʟᴜᴛɪᴏɴ :-

H = 12

Minutes = 30

Putting value in Above Told Formula we get :-

→ Angle = [ 30 * 12 - 30*(11/2) ]

→ Angle = [ 360 - 15*11 ]

→ Angle = [ 360 - 165 ]

→ Angle = 195° .

Now,

→ 180° = π Radian

→ 1° = (π/180)

→ 195° = (π/180) * 195 = (13π/12) Radian (Ans.)

Hence, Angle b/w Minute hand & Hour hand at 12:30 is (13π/12) Radian .

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Clock Chapter Reasoning Important :-

☛ The dial of the clock is circular in shape and was divided into 60 equal minute spaces..

☛ 60-minute spaces trace an angle of 3600. Therefore, 1minute space traverses an angle of 60..

☛ In 1 hour, Minute hand traverses 60-minute space or 3600 , Hour hand traverses 5-minute space or 300..

☛ The hands of the clock are perpendicular in 15-minute spaces apart....

☛ The hands of the clock are in straight line and opposite to each other in 30-minute spaces apart.

☛ The hands of the clock are in straight line when they coincide or opposite to each other.

☛ The hands of the clock are perpendicular to each other for 22 times in 12 hours and for 44 times in a day.

☛ The hands of the clock are opposite to each other for 11 times in 12 hours and 22 times in a day.

☛ The minute hand gain 55 minutes over hour hand per hour.

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Answer 2

$\rule{200}{3}$

GIVEN :-

The time in a clock is 12:30.

TO FIND :-

The radian measure of the angle between the minute hand of a clock and the hour hand when the time is 12:30.

SOLUTION :-

We know,

The angle in between each hour can be calculated as:- 360/12 = 30°

So, at 12:30, the hour hand will be between 12 and 1, and the minute hand will be at 6.

Now,

30 minutes = 1/2 hour

So, it means that the hour's hand has travelled = 30/2 = 15° beyond 12.

Difference of hours between the hour hand and the minute hand at 12:30 is 6 hrs.

So, the angle in between 12 (hour) and 30 (minutes at 6) is = 30 x 6 + 15 = 180 + 15 = 195°

We know,

Radian = (π/180)*degree

⇒Radian = (π/180)*195

⇒Radian = 13π/12

∴ So, the radian measure of the  angle between the minute hand of a clock and the hour hand at 12:30 is 13π/12 radians.

$\rule{200}{3}$