You will need

- Table of sines and cosines, table Bradis

Instruction

1

Denote the angles of a triangle with the letters a, B, and C, as shown in the figure. The angle BAC is 90º, the other two corners will be denoted by letters α and β. The legs of the triangle will be denoted by the letters a and b and the hypotenuse c.

2

Then sinα = b/c, cosα = a/c.

Similarly, the second acute angle of the triangle: sinβ = a/c, cosβ = b/c.

Depending on which sides are known to us, calculated the sines or cosines of angles and look at the table Bradis the value of α and β.

Similarly, the second acute angle of the triangle: sinβ = a/c, cosβ = b/c.

Depending on which sides are known to us, calculated the sines or cosines of angles and look at the table Bradis the value of α and β.

3

Finding one of the corners, you may recall that the sum of the internal angles of a triangle equal to 180º. Thus the sum of α and β equal to 180º - 90º = 90º.

Then, by calculating a value for α according to the table, unable to find β to use the following formula: β = 90 ° - α

Then, by calculating a value for α according to the table, unable to find β to use the following formula: β = 90 ° - α

4

If one of the unknown sides of a triangle, use the Pythagorean theorem: a2+b2=c2. Derive from it the expression for the unknown side using the other two and substitute into the formula for finding the sine or cosine of one of the corners.

Note

The height h divides the triangle ABC into two right-angled triangles similar to it. It triggered signs of similarity of triangles in three corners.

# Advice 2: How to find the hypotenuse in a right triangle

Call the hypotenuse side in a right triangle that lies opposite the right angle. The hypotenuse is the longest side in a right triangle. The other sides in a right triangle are called legs.

You will need

- Basic knowledge of geometry.

Instruction

1

The squared length of the hypotenuse equals the sum of the squares of the other two sides. That is, to find the square of the length of the hypotenuse you need to square the lengths of the legs and fold.

2

The length of the hypotenuse is equal to the square root of the square of its length. To find its length, extract the square root of the number equal to the sum of the squares of the legs. The resulting number will be the length of the hypotenuse.

Note

The length of the hypotenuse is a positive value, therefore, when extracting the root, radical expression must be greater than zero.

Useful advice

In an isosceles right triangle the length of the hypotenuse can be calculated by multiplying the leg to the root of the two.

# Advice 3: How to find acute angle in a right triangle

Directly

**the coal**, the triangle is probably one of the most famous, from a historical point of view, geometric shapes. Pythagorean pants" competition may be only a "Eureka!" Archimedes.You will need

- drawing a triangle;
- - the range;
- - protractor.

Instruction

1

As a rule, the vertices of the angles of a triangle are denoted by capital Latin letters (A, B, C), and the opposite side of the small Latin letters (a, b, c) or by the names of the vertices of the triangle constituting that side (AC, BC, AB).

2

The sum of the angles of a triangle is 180 degrees. In a rectangular

**triangle,**one angle (straight) will always be 90 degrees and the other acute, i.e. less than 90 degrees each. To determine the angle in a rectangular**triangle**is straight, measure with a ruler the sides of the triangle and determine the greatest. It is called the hypotenuse (AB) and is located opposite the right angle (C). The other two sides form a right angle are called legs (AC, BC).3

When it is determined what the angle is sharp, you can either measure the angle with a protractor, or calculated using mathematical formulas.

4

To determine the measure of the angle with a protractor, align the top (let's denote it by the letter A) with a special mark on the ruler in the center of the protractor, the side AC must coincide with its upper edge. Note on the circular part of the protractor to the point, through which the hypotenuse AB. The value at this point corresponds to the angle in degrees. If the protractor provided (2) the values for acute angle need to choose smaller, for the stupid - big.

5

The angle can be calculated by making simple mathematical calculations. You will need a basic knowledge of trigonometry. If you know the length of the hypotenuse AB and leg sun, calculate the value of the sine of the angle A: sin (A) = BC / AB.

6

The resulting value find the reference tables Bradis and determine what angle corresponds to the obtained number. This method was used by our grandmothers.

7

In our time, it is sufficient to take the calculator with the function of calculating trigonometric formulas. For example, the built-in Windows calculator. Run the application "Calculator" in the menu "View" select "Engineering". Calculate the sine of the desired angle, for example, sin (A) = BC/AB = 2/4 = 0.5

8

Switch calculator mode to inverse functions, click INV on the scoreboard calculator, then click calculate arcsine functions (on the scoreboard indicated, as sin to the minus one). In the window calculation will appear the following inscription: asind (0.5) = 30. I.e., the value of the desired angle of 30 degrees.

# Advice 4: How to calculate angle in a right triangle

Directly

**the coal**triangle are the two acute angles, the value of which depends on the lengths of the sides, and one angle is always the same value of 90°. To calculate the size of the acute angle in degrees, using trigonometric functions or theorems about the sum of the angles at the vertices of a triangle in Euclidean space.Instruction

1

Use trigonometric functions, if the conditions of the problem given only the dimensions of the sides of the triangle. For example, the lengths of the two legs (short sides adjacent to the right angle) you can calculate either of the two acute angles. The tangent of the angle (β), which is adjacent to the leg And can be found by dividing the length of the opposite side of him (In the leg) length of side A: tg(β) = B/A. But knowing the tangent, you can calculate and the corresponding value of the angle in degrees. This is a function of the arctangent: β = arctg(tg(β)) = arctg(b/A).

2

The same equation is possible to find the magnitude of the other acute angle, lying opposite the leg of A. Just change the designation of the parties. But you can do it in a different way, using another pair of trigonometric functions cotangent and arc cotangent. The cotangent of angle b is determined by dividing the length of the adjacent side And length of opposite: tg(β) = A/B. And the arc cotangent will help to extract from the received values the value of an angle in degrees: β = arсctg(сtg(β)) = arсctg(A/B).

3

If the baseline given the length of one of the other two sides (A) and the hypotenuse (C), to calculate angles use inverse sine and cosine inverse sine and inverse cosine. The sine of an acute angle β equal to the ratio of the length lying opposite leg to the length of the hypotenuse: sin(β) = B/C. So, to calculate the value of this angle in degrees use the following formula: β = arcsin(V/C).

4

And the value of the cosine of the angle β is determined by the ratio of the length adjacent to the top of the triangle leg And the length of the hypotenuse C. This means that to calculate the angle, in degrees, by analogy with the previous formula, it is necessary to use this equality: β = arccos(A/S).

5

The sum of angles of a triangle makes it unnecessary to use trigonometric functions if the point is given the value of one of the acute angles. In this case, to compute the unknown angle (α), just subtract from 180° the values of the two known angles straight (90°) and acute (β): α = 180° - 90° - β = 90° - β.