A right triangle is one in which one of the angles is 90 degrees and the other two are acute angles. Calculation of the perimeter of such triangle will depend on the amount of data known about it.
You will need
- Depending on the case, knowledge of two of the three sides of a triangle, as well as one of its acute angles.
Instructions
- Method 1. If all three sides are known triangle, then, regardless of whether the triangle is right-angled or not, its perimeter will be calculated as follows:
P = a + b + c, where, let's say,
c - hypotenuse;
a and b are legs. - Method 2. If only 2 sides are known in a rectangle, then, using the Pythagorean theorem, the perimeter of this triangle can be calculated using the formula:
P = v(a2 + b2) + a + b, or
P = v(c2 – b2) + b + c. - Method 3. Let a hypotenuse c and an acute angle ? be given in a right triangle, then the perimeter can be found in this way:
P = (1 + sin? + cos?)*s. - Method 4. It is given that in a right triangle the length of one of the legs is equal to a, and opposite it lies an acute angle?. Then calculating the perimeter of this triangle will be carried out according to the formula:
P = a*(1/tg ? + 1/sin ? + 1) - Method 5. Let us know the side a and the angle adjacent to it?, then the perimeter will be calculated as follows:
P = a*(1/сtg ? + 1/cos ? + 1)
The right triangle is a simple but extremely important figure for mathematics. Knowledge of its properties and the ability to operate with the basic parameters of a right triangle will allow you to cope with both school and real-life problems.
Geometry of a right triangle
Geometrically, a triangle is three points that do not lie on the same line, which are connected by segments. A right triangle is a figure whose two sides form a right angle. These sides are called the legs of the triangle, and the third, longest side is called the hypotenuse. The relationship between the squares of the legs and the hypotenuse is established by the Pythagorean theorem - one of the fundamental theorems of Euclidean geometry.
The relationships between the hypotenuse and legs also laid the basis for an entire branch of mathematics - trigonometry. Originally, sines and cosines were defined as functions of the angles of a right triangle, but in their modern meaning, trigonometric functions have been extended to the entire number line. Today, trigonometry is used in many areas of human activity: from astronomy and oceanography to financial market analysis and computer game development.
Right triangle in reality
The right triangle itself is found in reality at every corner, both literally and figuratively. The faces of tetrahedrons and prisms have the shape of a right triangle, which in reality turn into machine parts, ceramic tiles or roof slopes. A square is a drawing tool that a person first encounters in a geometry lesson; it has the shape of a right triangle and is used in design, construction and carpentry.
Perimeter of a triangle
Perimeter is a numerical estimate of the lengths of all sides of a flat geometric figure. The perimeter of an n-gon is found as the sum of the lengths of n sides. To determine the perimeter of a right triangle, use a simple formula:
a and b – legs, c – hypotenuse.
To calculate the perimeter of a triangle by hand, you would have to measure all three sides, perform additional trigonometric operations, or perform calculations using the Pythagorean theorem. Using an online calculator you just need to find out the following pairs of variables:
- two legs;
- leg and angle;
- hypotenuse and angle.
In school problems or in practice, you will be given initial data, so the calculator allows you to find the perimeter, knowing different pairs of parameters. In addition, the tool automatically calculates all other attributes of a right triangle, that is, the lengths of all sides and the magnitudes of all angles. Let's look at a couple of examples.
Examples from life
School task
Let's say in a school problem you are given a right triangle with a side length of 5 cm and an adjacent angle of 60 degrees. You need to find the perimeter of a geometric figure. The online calculator is accompanied by a drawing showing the sides and angles of a right triangle. We see that if leg a = 5 cm, then its adjacent angle is angle beta. This is an important point, because if you use the alpha angle for calculations, the result will be incorrect. We enter this data into the form and get a response in the form:
In addition to the perimeter itself, our program also determined the value of the opposite angle, as well as the length of the second leg and hypotenuse.
Flowerbed arrangement
Let's say you want to make a fence for a flower bed that has the shape of a right triangle. To do this, you need to know the perimeter of the figure. Of course, in reality you can simply measure all three sides, but it is easy to simplify your task and measure only two legs. Let them be 8 and 15 meters long. We enter this data into the calculator form and get the answer:
So, you will need to purchase materials to build 40 meters of fencing. Our calculator also calculated the length of the hypotenuse - 17 meters. The numbers 8, 15 and 17 form a Pythagorean triple - natural numbers that satisfy the conditions of the Pythagorean theorem.
Conclusion
Right triangles are widely used in everyday life, so determining the area or perimeter of a geometric figure will certainly be useful to you when solving school problems or everyday issues.
Perimeter of a triangle, as with any figure, is called the sum of the lengths of all sides. Quite often this value helps to find the area or is used to calculate other parameters of the figure.
The formula for the perimeter of a triangle looks like this:
An example of calculating the perimeter of a triangle. Let a triangle be given with sides a = 4 cm, b = 6 cm, c = 7 cm. Substitute the data into the formula: cm
Formula for calculating perimeter isosceles triangle will look like this:
Formula for calculating perimeter equilateral triangle:
An example of calculating the perimeter of an equilateral triangle. When all sides of a figure are equal, they can simply be multiplied by three. Suppose we are given a regular triangle with a side of 5 cm in this case: cm
In general, once all the sides are given, finding the perimeter is quite simple. In other situations, you need to find the size of the missing side. In a right triangle you can find the third side by Pythagorean theorem. For example, if the lengths of the legs are known, then you can find the hypotenuse using the formula: 
Let's consider an example of calculating the perimeter of an isosceles triangle, provided that we know the length of the legs in a right isosceles triangle.
Given a triangle with legs a =b =5 cm. Find the perimeter. First, let's find the missing side c. cm
Now let's calculate the perimeter: cm
The perimeter of a right isosceles triangle will be 17 cm.
In the case when the hypotenuse and the length of one leg are known, you can find the missing one using the formula: 
If the hypotenuse and one of the acute angles are known in a right triangle, then the missing side is found using the formula.
A right triangle is one in which one of the angles is 90 degrees and the other two are acute angles. Calculation perimeter such triangle will depend on the number of known data about him.
You will need
- Depending on the case, skill 2 of the 3 sides of the triangle, as well as one of its acute angles.
Instructions
1. Method 1. If all three sides are famous triangle, then, regardless of whether the triangle is right-angled or not, its perimeter will be calculated as follows: P = a + b + c, where, possibly, c is the hypotenuse; a and b are the legs.
2. Method 2. If only 2 sides are known in a rectangle, then, using the Pythagorean theorem, the perimeter of this triangle can be calculated using the formula: P = v(a2 + b2) + a + b, or P = v(c2 – b2) + b + c.
3. Method 3. Let a hypotenuse c and an acute angle? be given in a right triangle, then it will be possible to find the perimeter in this way: P = (1 + sin? + cos?)*c.
4. Method 4. It is given that in a right triangle the length of one of the legs is equal to a, and opposite it lies an acute angle?. Then the calculation perimeter this triangle will be carried out according to the formula: P = a*(1/tg ? + 1/sin ? + 1)
5. Method 5. Let us enter leg a and the angle adjacent to it?, then the perimeter will be calculated as follows: P = a*(1/сtg ? + 1/cos ? + 1)
Video on the topic
A right triangle is a special type of arbitrary triangle. Like any other triangle, it has three sides, but one of its angles must be 90 degrees. Once you have determined that a given triangle is a right triangle, you can begin to find its basic dimensions. One of the characteristics of a right triangle is its perimeter. Many geometry problems are devoted to finding the perimeter of a right triangle. Before we look at the main ways to find the perimeter of a right triangle, I would like to remind you that the perimeter of any geometric figure on a plane is equal to the sum of the lengths of all its sides. For all types of triangles, this statement can be written as the following expression:
where P is the perimeter of the triangle;
a, b, c - sides of the triangle.
In a right triangle, as mentioned above, there is a distinctive feature in the form of one of the angles of 90 degrees. The two sides of a triangle adjacent to a given angle are called legs. The side opposite the right angle is called the hypotenuse.
The unusual properties of the right triangle were discovered by Pythagoras, who discovered that the square of the hypotenuse of a right triangle is equal to the sum of the squares of its legs, which can be written as the expression:
A right triangle is a special type of arbitrary triangle. Like any other triangle, it has three sides, but one of its angles must be 90 degrees. Once you have determined that a given triangle is a right triangle, you can begin to find its basic dimensions. One of the characteristics of a right triangle is its perimeter. Many geometry problems are devoted to finding the perimeter of a right triangle.
Where P is the perimeter of the triangle;
A, b, c - sides of the triangle.
Based on the Pythagorean theorem, it became possible to determine the perimeter of a right triangle by its two sides of known length. If the lengths of the legs are known, then the perimeter of the triangle is determined by finding the value of the hypotenuse using the formula:
If only one of the legs and the length of the hypotenuse are known, then the perimeter of the triangle is determined by finding the value of the missing leg using the formula:
If in a right triangle only the length of the hypotenuse c and one of the acute angles α adjacent to it are known, then the perimeter of the triangle in this case can be determined by the formula:
In the case when the conditions of the problem specify the length of the leg a and the value of the acute angle α opposite it, then the perimeter of a right triangle in this case is calculated by the formula:
If a side a with an adjacent angle β is given, then the perimeter of the triangle can be calculated based on the expression:
P = a + b + c, where, let's say,
P = v(a2 + b2) + a + b, or
P = v(c2 – b2) + b + c.
P = (1 + sin? + cos?)*s.
P = a*(1/tg? + 1/sin? + 1)
P = a*(1/сtg? + 1/cos? + 1)
Other news on the topic:
How to find the perimeter of a right triangle
A right triangle is one in which one of the angles is 90 degrees and the other two are acute angles. The calculation of the perimeter of such a triangle will depend on the amount of data known about it.
Depending on the case, knowledge of two of the three sides of a triangle, as well as one of its acute angles.
Posting sponsor P&G Articles on the topic “How to find the perimeter of a right triangle” How to find the surface area of a pyramid How to find the perimeter if the area is known How to find the perimeter of an equilateral triangle
Method 1. If all three sides of the triangle are known, then, regardless of whether the triangle is right-angled or not, its perimeter will be calculated as follows:
P = a + b + c, where, let's say,
Method 2. If only 2 sides are known in a rectangle, then, using the Pythagorean theorem, the perimeter of this triangle can be calculated using the formula:
P = v(a2 + b2) + a + b, or
P = v(c2 – b2) + b + c.
Method 3. Let a hypotenuse c and an acute angle ? be given in a right triangle, then the perimeter can be found in this way:
P = (1 + sin? + cos?)*s.
Method 4. It is given that in a right triangle the length of one of the legs is equal to a, and opposite it lies an acute angle?. Then the calculation of the perimeter of this triangle will be carried out according to the formula:
P = a*(1/tg? + 1/sin? + 1)
Method 5. Let us know the side a and the angle adjacent to it?, then the perimeter will be calculated as follows:
P = a*(1/сtg? + 1/cos? + 1)
Other news on the topic:
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