# Advice 1: How to find the third side in a right triangle

Before we look at different ways of finding sides in a right triangle, let us take some notation. The leg is called the adjacent to the right angle side of a right triangle. The lengths of the legs let us denote a and b. The angles opposite sides a and b denote respectively through A and B. the Hypotenuse is, by definition, is the side of a right triangle that is opposite the right angle (with the other sides of the triangle the hypotenuse forms a sharp corner). The length of the hypotenuse is denoted by S.
Instruction
The angles opposite sides a and b denote respectively through A and B. the Hypotenuse is, by definition, is the side of a right triangle that is opposite the right angle (with the other sides of the triangle the hypotenuse forms a sharp corner). The length of the hypotenuse is denoted by S.
You will need:
Calculator.
Check which of the following cases corresponds to the condition of your problem and depending on this, refer to the relevant paragraph. Find out which values in the triangle you are aware of.
Use to calculate the sides of the following expression: a=sqrt(c^2-b^2), in that case, if you are aware of the magnitude of the hypotenuse and other leg. This expression is obtained from the Pythagorean theorem, which States that the square of the hypotenuse of a triangle is equal to the sum of the squares of the legs. The operator sqrt means square root. The sign "^2" means squaring.
Use the formula a=c*sinA if you know the hypotenuse (c) and the angle opposite to the desired side (this angle we have designated as A).
The expression a=c*cosB use for finding what to do if you know the hypotenuse (c) and the angle adjacent the desired side (this angle we have designated as B).
Calculate the leg by the formula a=b*tgA in the case when, given a side and angle b opposite to the desired side (this corner we have agreed to designate A).
If your problem side is not one of the described methods, most likely, it can be reduced to any of them.
Useful tips:
All these expressions are obtained from the well-known definitions of trigonometric functions, so even if you forget some of them, you can by simple operations, it quickly withdraw. Also, it is useful to know values of trigonometric functions for the most common angles 30, 45, 60, 90, 180 degrees.

# Advice 2: How to find acute angle in a right triangle

Directlythe 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 3: How to find the length of the hypotenuse in a right triangle

Call the hypotenuse the longest side in a right triangle, therefore, not surprising that in the Greek language this word is translated as "stretched". This side is always opposite the angle to 90° and the sides that form the angle are called the legs. Knowing the lengths of these sides and the magnitude of the acute angles in different combinations of these values, we can calculate the length of the hypotenuse.
Instruction
1
If you know the lengths of both legs of the triangle (A and b), then use to find the length of the hypotenuse (C) is probably the most famous on the planet a mathematical postulate - the Pythagorean theorem. It States that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, from which it follows that you should calculate the square root of the sum of squared lengths of two known sides: C=√(A2+B2). For example, if the length of one leg is 15 inches and the other 10 centimeters, the length of the hypotenuse will be approximately 18,0277564 centimeters, as √(152+102)=√(225+100)= √325≈18,0277564.
2
If you know the length of only one of the legs (A) in a right triangle, and the angle lying opposite it (α), the length of the hypotenuse (C) can be determined using one of the trigonometric functions - sine. To do this, divide the length of the known side by the sine of the known angle: C=A/sin(α). For example, if the length of one of the legs is equal to 15 centimeters and the angle at the opposite vertex of the triangle is 30°, the length of the hypotenuse is equal to 30 centimeters, as 15/sin(30°)=15/0,5=30.
3
If in a right triangle, we know the value of one of the acute angles (α) and the length of the adjacent leg (B), to calculate the length of the hypotenuse (C) you can use another trigonometric function, the cosine. You should divide the length of the known leg to the cosine of the known angle: S=V/ cos(α). For example, if the length of this side is 15 centimeters and the magnitude of the acute angle, the Annex, is 30°, the length of the hypotenuse will be approximately 17,3205081 centimeters, as 15/cos(30°)=15/(0,5*√3)=30/√3≈17,3205081.
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