(ii) The angle between hour hand and minute hand at 2:30 is ……….
Answers
Answer:
2:30= 105°
OBTUSE ANGLE
Step-by-step explanation:
As we all know the 12 division of a 360 circle gives each division 30 degrees.
So at 2:30 p.m. the minute hand will be at 6 and hour hand will be exactly between 2 & 3, because it is 30 minutes remaining in 3 and 30 minutes completed over 2.
If we take 12 at 0 degrees than 6 will be at 180 degrees. Now 2 will be at 60 degrees from 12 and 3 will be at 90 degrees from 12. Therefor the angle of hour hand from 12 will be (60+90)/2 = 75 degrees.
Now substracting angles of hands w.r.t 0 degrees (at 12) ,
180 - 75 =105 degrees in clockwise direction from hour hand and minute hand.
Given:
Hands of the clock showing time = 2:30
To find:
The angle between hour hand and minute hand at 2:30 =?
Solution:
=> The angle between the two hands of the clock can be found using the following steps:
=> The clock shows 12 hours in a day and it is circular therefore one complete rotation is 360°.
=> Every hour of the clock is at an equal angle distance divided by 30°.
Step 1: Angle of hour hand from 12:
=> When it is 2:30 we know that the hour hand of the clock is exactly between 2 and 3.
= 30° × 2
= 60° + 15°
= 75°
Step 2: Angle of the minute hand from 12
=> When the minute hand shows 30 minutes the minute hand of the clock is exactly at 6.
=> It forms a straight angle.
= 30° × 6
= 180°
Step 3: Difference of angle
The angle between the hour hand and minute hand =
= (Angle of minute and from 12 - Angle of hour hand from 12)
The angle between the hour hand and minute hand = 180° - 75°
The angle between the hour hand and minute hand = 105°
Hence, the angle between the hour hand and minute hand at 2:30 is 105°.