let's learning in here: lines and angles

MEASURE OF ANGLES
The unit measurement of angles is degree, which is denoted by $\aa$ . The measure of the angle for one rotation is $360^{\circ}$ .
One full rotation of minute hand of a wall clock is equal to 60 minutes. 1 minute is equal to 60 seconds. You can also find the same thing on degree’s unit.
1 degree = 60 minutes, denoted by $1^{\circ}= {60}'$
1 minute = 60 seconds, denoted by ${1}'={60}''$
Example:
Solve the following problems.
1. ${1}''= \cdots {}'$
2. $6^{\circ}=\cdots {}'$
3. ${45}'=\cdots ^{\circ}$
4. $3^{\circ}=\cdots{}''$
5. ${90}''=\cdots ^{\circ}$ .
SOLUTION:
1. We have ${1}'= {60}''$ so that ${1}''=\frac{1}{60}minutes$ .
2. We have $1^{\circ}= {60}'$ so that $6^{\circ}= 6 \times {60}'={360}'$ .
3. We have ${1}'=\frac{1}{60}degrees,$ so that ${45}'= 45\times \frac{1}{60}degrees =0.75^{\circ}$ .
4. We have $1^{\circ}={3600}''$ so that $3^{\circ}=3\times{3,600}''={10,80}''$ .
5. We have ${1}''=\frac{1}{3,600}$ degrees, so that ${90}''=90\times \frac{1}{3,600}$ degrees = $0.025^{\circ}$ .
3. ADDITION AND SUBTRACTION ON ANGLES.
The followings should be considered whenever we want to add and subtract the angles.

The counterclockwise rotation of an angle results the positive value of its measure.
The clockwise rotation of an angle results the negative value of its measure.

EXAMPLE:
Determine the result of:
1. $65^{\circ}+ 30^{\circ}-25^{\circ}$ .
2. $3^{\circ}{15}'{40}''+20^{\circ}{10}'{20}''$ .
3. $16^{\circ}{14}'{28}''+23^{\circ}{45}'{32}''$ .
4. $62^{\circ}{49}'{32}''-43^{\circ}{34}'{17}''$ .
5. $53^{\circ}{28}'{17}''-42^{\circ}{16}'{33}''$
SOLUTION:
1. $65^{\circ}+ 30^{\circ}-25^{\circ}$ = $95^{\circ}-25^{\circ}=70^{\circ}$ .
2. $3^{\circ}{15}'{40}''+20^{\circ}{10}'{20}''$
= $(3+20)^{\circ}+{(15+10)}'+{(40+20)}''=23^{\circ}{25}'{60}''=23^{\circ}{26}'$ .
3. $16^{\circ}{14}'{28}''+23^{\circ}{45}'{32}''$ = $(16+23)^{\circ}+{(14+45)}'+{(28+32)}''$
= $"39^{\circ}</p$ .
4. $62^{\circ}{49}'{32}''-43^{\circ}{34}'{17}''$ = $(62-43)^{\circ}+{(49-34)}'+{(32-17)}''$
= $19^{\circ}{5}'{15}''$
5. $53^{\circ}{28}'{17}''-42^{\circ}{16}'{33}''$
= $53^{\circ}{27}'{77}''-42^{\circ}{16}'{33}''$
= $(53-42)^{\circ}+{(27-16)}'+{(77-33)}''$
= $9^{\circ}11'44''$ .

let's learning in here

Senin, 05 Maret 2012

lines and angles

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