How to find the height in a right triangle

How to find the height in a right triangleAny school program includes such subject as geometry. Each of us, being a student, studied this discipline and solved certain tasks. But for many people, school years were left behind and some of the acquired knowledge was erased from memory.

What to do if you suddenly need to find an answer to a question from a school textbook, for example, how to find the height in a right-angled triangle? In this case, a modern advanced computer user will first open the Internet and find information of interest to him.
 

Triangle Basic Information

 
This geometrical figure represents 3 segments interconnected at the end points, and the points of contact of these points are not on one straight line. The segments that make up the triangle are called its sides. The junction of the sides form the tops of the figure, as well as its corners.

Types of triangles depending on angles

This figure can have three types of angles: sharp, blunt and straight. Depending on this, among the triangles there are the following types:

  1. The acute angle is the one in which all sides, touching at the vertices, form angles less than 90º in size.
  2. The obtuse angle is a figure that has 1 angle more than 90º. It is called blunt, and the 2 remaining angles in such a triangle have a magnitude less than 90º.
  3. Rectangular - in such a figure, the two sides at the point of contact form an angle with an indicator of exactly 90º.How to find the height in a right triangle

 

Types of triangles depending on the length of the sides

 
As mentioned earlier, this figure is formed from three segments. Based on their size, the following types of triangles are distinguished:

  1. Equilateral - these are those in which the length of each side has the same size. Such triangles are also called "correct".
  2. Isosceles - in these geometric figures, only 2 sides are equal to each other.
  3. Versatile - in such triangles, each of the 3 segments forming sides, has a different length.How to find the height in a right triangle

 

How to find the height of a right triangle

 
Two identical sides of a right triangle, forming a right angle at the point of contact, are called legs. The segment that connects them is called the "hypotenuse."To find the height in this geometric figure, it is necessary to lower the line from the vertex of the right angle to the hypotenuse. In this case, this line should divide the angle of 90º exactly in half. Such a segment is called a bisector.How to find the height in a right triangle

The picture above showsright triangle,heightwhich we have to calculate. This can be done in several ways:

  1. The value of this indicator can be calculated by one of the following formulas:How to find the height in a right triangle
  2. You can use another method and find the height through the area of ​​the figure. So, the area of ​​a triangle is calculated by the formula:How to find the height in a right triangle
  3. Since the area of ​​such a figure is ½ of the product of the legs, the following formulas will help us in the calculations:How to find the height in a right triangle
  4. If we represent equal sides as a and b, and the segment connecting them as with, then we get the following formula:How to find the height in a right triangle

If you draw a circle around the triangle and draw a radius, its value will be half the size of the hypotenuse. Based on this, the height of a right triangle can be calculated by the formula:How to find the height in a right triangle

In this article, we explained how to calculate the height of a right-angled triangle in various ways. Depending on what values ​​are given to you in the original task, you can choose the most suitable variant of calculations for yourself.


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