Sexagesimal system

Index Angles Time Converting to another system Adding and Subtracting Exercises
Sexagesimal system
Matematicas 2o E.S.O.
Alberto Pardo Milanes
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1 Angles
2 Time
3 Converting
4 Adding and Subtracting
5 Exercises
Alberto Pardo Milanes Sexagesimal system

Angles

Angles
What's an angle? Measure an angle
Given two intersecting lines, the point of
intersection is called the vertex and the
amount of rotation about the vertex re-
quired to bring one line into correspondence
with the other is called the angle between
them.
There are several ways to measure the size of an angle. One way is
to use units of degrees: In a complete circle there are three hundred
and sixty degrees (one full rotation corresponds to 360 degrees).

Angles
Some angles
Half a full rotation is called a straight angle that is 180 de-
grees, and a quarter of a full rotation is called a right angle
(90 degrees). An angle less than 90 degrees is called an acute
angle, an angle greater than 90 degrees and less than 180
degrees is called an obtuse angle, and an angle greater than
180 degrees and less than 360 degrees is called a re
ex angle.

Angles
Using the proctartor
Acute angle Right angle
Obtuse angle Straight angle

Angles
Express an angle
You can express angles to any precision using decimal numbers.
Example: 4 degrees and a half=4.5 degrees.
There is another way to state the size of an angle, and that is by
subdividing a degree. The degree is divided into sixty parts called
minutes. These minutes are further divided into sixty parts called
seconds.
In a full circle there are 360 degrees, each degree is split up into 60
parts called minutes (each part being 1=60 of a degree), each
minute is split up into 60 parts called seconds (each part being
1=60 of a minute).
Examples: 1 degree is 60 minutes, so ;5 degrees=;5 60 = 30
minutes, so 4.5 degrees is equal to 4 degrees and 30 minutes.
14 degrees, 22 minutes and 55 seconds is usually written this
way: 14o 220 5500
.

Time

To measure time we can use hours: In a day there are twenty-four
hours.
You can express time to any precision using decimal numbers.
There is another way to state the amount of time, subdividing an
hour. The hour is divided into sixty parts called minutes. These
minutes are further divided into sixty parts called seconds.
In a day there are 24 hours, each hour is split up into 60 parts
called minutes (each part being 1=60 of an hour), each minute is
split up into 60 parts called seconds (each part being 1=60 of a
minute).
Example: 18 hours,51 minutes and 42 seconds is usually written
this way: 18hr 51min 42sec.

Converting

Converting
Sexagesimal to decimal
To convert sexagesimal format to decimal format divide the
seconds by three thousand six hundred, then add it to the minutes
divided by sixty, and

nally add the degrees. To convert time do
the same.
Example: 22o 540 1800 is written in the sexagesimal system. To
convert it to decimal: 18=3600+54=60+22 = 0;005+0;9+22 =
22;905o.

Converting
Decimal to sexagesimal
To convert decimal format to sexagesimal format the whole units
of degrees will remain the same, then multiply the decimal by 60,
the whole number becomes the minutes, take the remaining
decimal and multiply by 60, the resulting number becomes the
seconds. Seconds can remain as a decimal. Take your three sets of
numbers and put them together, using the symbols for degrees (o),
minutes (0), and seconds (00). To convert time do the same.
Example: 35;245o is written in the decimal system. To convert it
to sexagesimal: 35 are the degrees, 0;245 60 = 14;7 so 14 are the
minutes, 0;7 60 = 42 so 42 are the seconds. 35;245 degrees are
35o 140 4200.

Adding and Subtracting

To add or subtract angles or time, you must add or subtract the
units separately. But you may need to do some adjusting:
the hours can not end up 24 or more,
the degrees can not end up 360 or more,
the minutes can not end up 60 or more,
and the seconds can not end up 60 or more.
Negative numbers can not be used.

Adding
Add the hours. If the hours are 24 or more, then you have to
subtract 24 from the hours and increase the number of days by
one. Add the minutes. If the minutes are 60 or more, subtract 60
from the minutes and increase the number of hours by one. Add
the seconds. If the seconds are 60 or more, subtract 60 from the
seconds and increase the number of minutes by one. To add angles
do the same method.

Adding
Example: To add 18hr 55min + 9hr 21min:
18 hr 55 min
+ 9 hr 21 min
27 hr 76 min
1 day 3 hr 76 min
1 day 4 hr 16 min
Add the hours: 18 + 9 = 27. The hours are 24 or more, so we
subtract 24 from the hours (27 24 = 3hr) and increase the
number of days by one. Add the minutes: 55 + 21 = 76. The
minutes are 60 or more, so subtract 60 from minutes (76 60 =
16min) and increase the number of hours by one (3 + 1 = 4hr).
So 18hr 55min + 9hr 21min= 1day 4hr 16min.

Subtracting
Subtract the hours, if the hours are negative, add 24 to the hours
and subtract 1 from the days. Subtract the minutes, if the minutes
are negative, add 60 to the minutes and subtract 1 from the hours.
Subtract the seconds, if the seconds are negative, add 60 to the
seconds and subtract 1 from the minutes.

Subtracting
Example: To subtract 12hr 30min - 7hr 55min:
12 hr 30 min
- 7 hr 55 min
11 hr 90 min
- 7 hr 55 min
4 hr 35 min
Subtract the hours: 12 7 = 5. Subtract the minutes: 30 55 =
25. The minutes are negative, so subtract 1 from hours and
increase the number of minutes by sixty (30 + 60 = 90min). So
12hr 30min - 7hr 55min =
=11hr 90min - 7hr 55min= 4hr 35min.

Exercises

Exercises
Exercise 1
Find

ve objects in your classroom that have all kind of angles
angles but no right angles.

Exercises
Exercise 2
Using a set square is easy to draw a right angle, a 30o angle, a 45o
angle or a 60o angle. Use a set square to draw a 15o angle and a
75o angle.
30o angle 45o angle 60o angle

Exercises
Exercise 3
Measure these angles:

Exercises
Exercise 4
Write down the following amounts:
12o 110 1200:
145o 230 300:
3hr 25min 28sec:
16hr 46min 50sec:

Exercises
Exercise 5
Jane works six hours a day from Monday till Friday, and one hour
less on Saturday. How many hours does she work a week?

Exercises
Exercise 6
At 13:45 AM, Peter went to have lunch at his friend Paul's house.
His mother told him to be back in two and a half hours. At what
time does Peter have to be home?

Exercises
Exercise 7
Thirty days have September, April, June, and November; All the
rest have thirty-one, Save February, with twenty-eight days clear,
And twenty-nine each leap year. How many days are there in one
leap year? How many hours? How many minutes? How many
seconds?

Exercises
Exercise 8
Two angles are complementary if the sum of their measures is 90o.
Find two complementary angles measuring exactly the same.

Exercises
Exercise 9
Two angles are supplementary if the sum of their measures is 180o.
Find two supplementary angles being the measure of the big one
three times the measure of the small one.

Exercises
Exercise 10
Charles rode his bike on Monday and Thursday. He spend 1hr
36min 48sec riding on Monday and 1hr 32min 25sec riding on
Thursday How much time did he ride over the two days in total?

Exercises
Exercise 11
The interior angles of a triangle always add up to 180o. If two
angles of a triangle measure 21o 240 and 86o 490. What is the
measure of the third angle?

Exercises
Exercise 12
Spencer got on the train to get to the airport at 11:23. He spent
42 min in the train. It took him 25 min to get his plane ticket and
He spent 1 h 6 min waiting for the plane to take o. At what time
did the plane take o?

Exercises
Exercise 13
A tv show started at 20:25 and it ended at 23:30. How long did
the show last for?

Sexagesimal system

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