Instruction

1

To calculate the value of an acute angle in a right triangle, you need to know the values of all its sides. Take the necessary notation for the elements of a right triangle:

c is the hypotenuse;

a,b are the legs;

A – Acute angle, which is opposite side b;

B – Sharp corner, which is opposite side a.

c is the hypotenuse;

a,b are the legs;

A – Acute angle, which is opposite side b;

B – Sharp corner, which is opposite side a.

2

Calculate the length of the sides of the triangle, which is unknown, using the Pythagorean theorem. If you know a leg and the hypotenuse is c, we can calculate the side b; why subtract the square of the length of the hypotenuse c, the square of the length of side a, then remove from the resulting values of the square root.

3

Similarly, you can calculate the side a, if we know the hypotenuse c and side b, from the c square of the hypotenuse subtract the square of side b. Then from the result extract the square root. If you know two sides and need to find the hypotenuse, add the squares of the lengths of the legs and from the resulting values, extract the square root.

4

The formula for trigonometric functions calculate the sine of the angle A: sinA=a/c. In order for the result to be more accurate, use a calculator. The resulting value is rounded to 4 digits after the decimal point. Similarly, find the sine of angle B, what is sinB=b/c.

5

Using the "four-digit mathematical tables" Bradis, find the values of angles in degrees using the known values of the sines of these angles. To do this, open table VIII "Table" Bradis and look at the value previously calculated sinuses. In this table the first column "A" has a value of the desired angle in degrees. In the column, where the value of the sinus, in the upper line "A", find the minutes value for the angle.

Note

Table Bradis contain values limited to four digits after the decimal point, so round obtained in the course of computing the values up to this limit.

Useful advice

To determine the angle after calculation of the value of its sine, you can use a calculator that has trigonometric functions.

# Advice 2: How to calculate the square root

Calculating the square roots scared some students at first. Let's see how they need to work and what to pay attention to. Also we give their properties.

Instruction

1

About the use of the calculator will not speak, although, of course, in many cases it is simply necessary.

So, the square root of the number x is the number y, which squared gives the number x.

Definitely need to remember one very important point: the square root is computed only from positive numbers (not complex take). Why? See the definition written above. The second important point: the result of the root extraction if there are no additional conditions in the General case there are two integers: +y and -y (in the General case, the module y), as both of them squared gives the original number x, which does not contradict the definition.

The square root of zero is zero.

So, the square root of the number x is the number y, which squared gives the number x.

Definitely need to remember one very important point: the square root is computed only from positive numbers (not complex take). Why? See the definition written above. The second important point: the result of the root extraction if there are no additional conditions in the General case there are two integers: +y and -y (in the General case, the module y), as both of them squared gives the original number x, which does not contradict the definition.

The square root of zero is zero.

2

Now, with regard to specific examples. For small numbers the squares (and hence the roots as the inverse operation) it is best to remember the multiplication table. I'm talking about the numbers from 1 to 20. This will save your time and help in assessing the possible value of the desired root. For example, knowing that the root of 144 = 12, and the root of 13 = 169, we can estimate that the root of the number 155 is between 12 and 13. A similar evaluation can be applied for larger numbers, their only difference is the complexity and execution time of these operations.

Also, there is another simple fun way. Let's show it on example.

Suppose there is a number 16. Find out which number is his root. To do this, we successively subtract of the 16 primes and count the number of operations performed.

So, 16-1=15 (1), 15-3=12 (2), 12-5=7 (3), 7-7=0 (4). 4 operations – the required number 4. The essence is to carry out the subtraction as long as the difference does not become equal to 0 or will simply be deducted less than the next Prime number.

The disadvantage of this method is that thus it is possible to find only the integer part of the root, but not all of its exact meaning completely, but sometimes with a precision of estimation or errors of computation, and this is enough.

Also, there is another simple fun way. Let's show it on example.

Suppose there is a number 16. Find out which number is his root. To do this, we successively subtract of the 16 primes and count the number of operations performed.

So, 16-1=15 (1), 15-3=12 (2), 12-5=7 (3), 7-7=0 (4). 4 operations – the required number 4. The essence is to carry out the subtraction as long as the difference does not become equal to 0 or will simply be deducted less than the next Prime number.

The disadvantage of this method is that thus it is possible to find only the integer part of the root, but not all of its exact meaning completely, but sometimes with a precision of estimation or errors of computation, and this is enough.

3

Some basic properties: the root of the sum (difference) is not equal to the sum (difference) of the roots, but the root of the product of (private) equal to the product of (private) roots.

The root of the square of the number x is the number x.

The root of the square of the number x is the number x.

# Advice 3: How to calculate angle in triangle

From the school course of plane geometry known definition: a triangle is a geometrical figure consisting of three points not lying on one straight line and three segments that connect pairs of these points. Points are called vertices, and line segments – the sides of the triangle. Share the following types of triangles: acute-angled, obtuse-angled and rectangular. Also klassificeret triangles by sides: isosceles, equilateral and scalene.

Depending on the form of a triangle, there are several ways to measure its angles, sometimes it is enough to know only the shape of a triangle.

Depending on the form of a triangle, there are several ways to measure its angles, sometimes it is enough to know only the shape of a triangle.

Instruction

1

The triangle is rectangular if it has the right angle. In the measurement of its angles, you can use trigonometric calculations.

In this triangle the angle ∠C = 90º, as a direct, knowing the lengths of the sides of a triangle, the angles ∠A and ∠B are computed by the formulas: cos∠A = AC/AB cos∠B = BC/AB. Degree measures of the angles can be found by referring to the table of cosines.

In this triangle the angle ∠C = 90º, as a direct, knowing the lengths of the sides of a triangle, the angles ∠A and ∠B are computed by the formulas: cos∠A = AC/AB cos∠B = BC/AB. Degree measures of the angles can be found by referring to the table of cosines.

2

The triangle is called equilateral if all the sides are equal.

In an equilateral triangle all the angles are equal to 60º.

In an equilateral triangle all the angles are equal to 60º.

3

In the General case, for finding the angles in an arbitrary triangle we can use the theorem of cosines

cos∠α = (b2 + c2 - a2) / 2 • b • c

Degree measure of an angle can be found by referring to the table of cosines.

cos∠α = (b2 + c2 - a2) / 2 • b • c

Degree measure of an angle can be found by referring to the table of cosines.

4

A triangle is called isosceles if two sides are equal, the third side is called the base of the triangle.

In an isosceles triangle the angles at the base are equal, i.e. ∠A = ∠B. One of the properties of a triangle is that the sum of its angles always equals 180º, so calculating the cosine theorem, the angle ∠C, the angles ∠A and ∠B we can calculate: ∠A = ∠B = 180º - ∠C)/2

In an isosceles triangle the angles at the base are equal, i.e. ∠A = ∠B. One of the properties of a triangle is that the sum of its angles always equals 180º, so calculating the cosine theorem, the angle ∠C, the angles ∠A and ∠B we can calculate: ∠A = ∠B = 180º - ∠C)/2

# Advice 4: How to calculate the sine of the angle

When you have to deal with solving applied problems involving trigonometric functions, most commonly required to compute values

**of the sine**or co**sine**of the specified**angle**.Instruction

1

The first option is classic, using paper, protractor, and pencil (or pen).By definition the sine

**of an angle**is the ratio of the opposite leg to the hypotenuse of a right triangle. That is, to calculate the value you need with the help of a protractor to construct a right triangle one of whose angles is equal to the sine of which you are interested in. Then measure the length of the hypotenuse and opposite side and divide the second into first with the desired degree of accuracy.2

The second option is the school. From school we all remember the tables Bradis" containing thousands of values of trigonometric functions from different angles. You can look for as a paper edition and its electronic equivalent in pdf format - they are in the network. Finding a table to find the value of

**sine**of the desired**angle**is not difficult.3

The third option is optimal. If you have access to a computer, you can use a standard calculator Windows. It should be switched to advanced mode. To do this, under "View" menu, select "Engineering." View of the calculator will change - it will, in particular, the buttons to compute trigonometric functions.Now enter the value

**of angle**, sine of which you want to calculate. You can do it from the keyboard and clicking the mouse cursor on the keys of the calculator. And you can just copy and paste the value (CTRL + C and CTRL + V). Then select a unit of measure, which must be calculated the answer for trigonometric functions it can be radians, degrees or happy. This is done by selecting one of three values switch located below the input field calculated value. Now by pressing the button labeled "sin", will get an answer to your question.4

The fourth option is the most modern. In the era of the Internet in the network there are resources that offer you to deal with almost every encountered in life the problem. Online calculators trigonometric functions with user friendly interface, more advanced functionality is not difficult. The best of them suggest to calculate not only the values of the individual functions, but rather complicated expressions of several functions.