Hamilton High School starts at 8.30am and finishes at 3.30pm each day. The number of time the hour and minute hand form a right angle on the school clock during the day is?
Is it 13 or 14 but why is it so?
Hello, clarebear14!
There is no formula for this problem.Hamilton High School starts at 8:30 am and finishes at 3:30 pm each day.
The number of times the hour and minute hand form a right angle
on the school clock during the day is ...?
. . We must make a series of sketches.
I found twelve times.
The times (approximate) are: .9:00, 9:30, 10:05, 10:35, 11:10, 11:45,
. . 12:15, 12:50, 1:20, 1:55, 2:25, 3:00
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Note: Three-thirty is not included.
At 3:30, the hour hand is halfway between 3 and 4,
. . forming a 105° angle with "12".
So the minute hand would form a 195° angle with "12",
. . indicating a time after three-thirty.
The time period between 2 right angles is $\displaystyle \frac6{11} \ hours$. (Half an hour plus the half of $\displaystyle \frac1{11}$ hour)
Divide the time span from 08:30 am to 03:30 pm = 7 hours by $\displaystyle \frac6{11}$ you'll get $\displaystyle \left(12 + \frac56\right)\ times$
So it happens 12 times that the hands of the clock form a right angle.