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3.04.2016

What are the angles of the triangle?

Q: What are the angles of the triangle ABC, if the sum of the angles A and B is equal to 100 degrees, the sum of the angles B and C equal to 120 degrees?
The triangle and the angles. Mathematics For Blondes.
The triangle and the angles
 We have two sum of two angles:

A + B = 100
B + C = 120

The sum of angles in a triangle is 180 degrees.

A + B + C = 180

Substitute in this formula the sum of two angles and find the third angle:

100 + C = 180
C = 180 - 100
C = 80

The second sum of the angles substitute angle C:

B + 80 = 120
B = 120 - 80
B = 40

The first sum of angles substitute angle B:

A + 40 = 100
A = 100 - 40
A = 60

A: The angles of the triangle are equal: A=60 degrees, B=40 degrees, C=80 degrees.

If we substitute in the second sum angles of a triangle, then the solution would be:

A + 120 = 180
A = 180 - 120
A = 60

60 + B = 100
B = 100 - 60
B = 40

60 + 40 + C = 180
C = 180 - 60 - 40
C = 80

The third variant of the decision:

We find the angle A of the first sum.

A + B = 100
A = 100 - B

We find the angle C of the second sum.

B + C = 120
C = 120 - B

Substitute the found angles to the general formula:

A + B + C = 180
(100 - B) + B + (120 - B) = 180
100 - B + B + 120 - B = 180
B - 2B = 180 - 100 - 120
-B = -40
B = 40

A = 100 - 40
A = 60

C = 120 - 40
C = 80

Conclusion: if the problem is solved correctly, the result does not depend on the method of solution.

What time is it now?

Q: From the beginning of the day it took 3/4 days. What time is it now?

The day has 24 hours. Multiply the fraction by the number of hours in the day.

24 * 3/4 = 18 (hours)

From the beginning of the day it took 18 hours. Now we can calculate the time.

18:00 - 12:00 am = 6:00 pm

A: Now 18:00 or 6:00 pm.

3.01.2016

How to simplify?

Help simplify the mathematical expressions:

1) 5.25x+7.56+4.98x-1.25x+0.02x
2) 12.78x+3.84x+2.22x+1.16x-0.3x


It is not hard. We believe that X's - it's rabbits. Why rabbits are not the whole? Their evil Putin nibbled. The numbers - it's just a numbers. Now we add up the rabbits with rabbits. The numbers add up separately. Perform a permutation terms, make it easier to summarize.

1) 5.25x+7.56+4.98x-1.25x+0.02x=
=(5.25x-1.25x)+(4.98x+0.02x)+7.56=
=4x+5x+7.56=9x+7.56

2) 12.78x+3.84x+2.22x+1.16x-0.3x=
=(12.78x+2.22x)+(3.84x+1.16x)-0.3x=
=15x+5x-0.3x=19.7x

Here's how it's simple.

2.15.2016

Find the angles of an isosceles triangle

Find the angles of an isosceles triangle if the angle opposite the base, at 24 degrees less than the angle at the base of the triangle.

The triangle is isosceles. In an isosceles triangle the angles at the base are equal. The sum of the angles of a triangle is 180 degrees.

Let the angle at the base through X. Then the angle opposite the base, is equal to X-24. We write the formula for the sum of angles of a triangle and find the X:

2х+х-24=180
3х=180+24
х=204/3
х=68


Now we find the third angle:

х-24=68-24=44

Make a check: 2*68+44=136+44=180

Answer: the corners of triangle are equal to 68, 68 and 44 degrees.

11.12.2015

The sine values

The unit circle can be considered not only for individual trigonometric functions, but also under the microscope each function separately. Here are the sine values for different angles.

sin 0. Mathematics for blondes.
sin 0

sin 30. sin p/6, sine 1/6 pi. Mathematics for blondes.
sin 30
sin 45, sin p/4, sine pi/4. Mathematics for blondes.
sin 45
sin 60, sine p/3, sin pi/3. Mathematics for blondes.
sin 60
sin 90, sin p/2, sin pi/2, sine 1/2 pi. Mathematics for blondes.
sin 90
sin 120, sin 2p/3, sin 2pi/3, sine 2/3 pi. Mathematics for blondes.
sin 120
sin 135 degrees, sin 3p/4, sin 3pi/4, sine 3/4 pi radians. Mathematics for blondes.
sin 135
sin 150, sine 5/6 pi radians, sin 5p/6, sin 5 pi by 6. Mathematics for blondes.
sin 150
sin 180, sin pi. Mathematics for blondes.
sin 180
sin 210, sin 7p/6, sin 7/6 pi. Mathematics for blondes.
sin 210
sin 225, sin 5/4 pi, sin 5p/4. Mathematics for blondes.
sin 225
sin 240, sin 4p/3, sine 4 pi division by 3 radians, sin 4/3 pi. Mathematics for blondes.
sin 240
sin 270, sin 3pi/2, sine 3/2 pi. Mathematics for blondes.
sin 270
sin 300, sin 5p/3, sin 5/3 pi. Mathematics for blondes.
sin 300
sin 315, sin 7pi/4, sin 7/4 pi. Mathematics for blondes.
sin 315
sin 330, sin 11pi/6, sin 11/6 pi. Mathematics for blondes.
sin 330
sin 360, sin 2pi, sine 2 pi radians. Mathematics for blondes.
sin 360

The unit circle is like a movie that shows us mathematics. Here you see some pictures of the cult TV series.

11.11.2015

Unit circle

Mathematicians consider themselves clever and all the rest. But not all of us are as smart as mathematics. The unit circle mathematics invented for themselves. For those who are just beginning to study mathematics, I suggest a simpler version - separately cosines and sines separately.

If we remove from the unit circle all that relates to the sine, we get the unit circle cosines.

Unit circle cosines. Cos 0, cos 30, cos 45, cos 60, cos 90. Mathematics for blondes.
Unit circle cosines

If we remove from the unit circle everything about cosines, we get a unit circle sinuses.

Unit circle sinuses. Sin 0, sin 30, sin 45, sin 60, sin 90. Mathematics for blondes.
Unit circle sinuses

Now, you will not confuse the values of sines and cosines.

11.10.2015

Degrees, minutes, seconds

I was write: "Help me to understand. It is necessary to determine how many degrees, minutes, and seconds contains 4563 seconds corner. Only by actions, and I completely confused."

No harly-barly! We sit quietly and remember that one minute contains 60 seconds, in one degree contains 60 minutes. Now we pimenyaem our knowledge into practice. Transform seconds in a minutes.

4563 : 60 = 76.05 minutes

Determine how many seconds we leave intact:

4563 - 60 * 76 = 4563 - 4560 = 3 seconds

Now 76 minutes translate into degrees, still sadly dividing by 60:

76 : 60 = 1.26667 degrees

We calculate how many minutes do not fit into the clothes degrees:

76 - 60 * 1 = 76 - 60 = 16 minutes

Now our suffering ended and we in good conscience can write the final result:

4563 seconds = 1 degree 16 minutes 3 seconds

Checking? We translate everything back to the second:

1 * 60 * 60 + 16 * 60 + 3 = 3600 + 960 + 3 = 4563

As the math, the conversion is correct.