# Math Help - Right angles and clock

1. ## Right angles and clock

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?

2. Hello, clarebear14!

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 ...?
There is no formula for this problem.
. . 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.

3. Originally Posted by clarebear14
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?
The time period between 2 right angles is $\frac6{11} \ hours$. (Half an hour plus the half of $\frac1{11}$ hour)

Divide the time span from 08:30 am to 03:30 pm = 7 hours by $\frac6{11}$ you'll get $\left(12 + \frac56\right)\ times$

So it happens 12 times that the hands of the clock form a right angle.