# How to find the base of a triangle?

Geometry - one of the school subjects, which is useful in the future for all. For one simple reason - geometry, and subsequently stereometry develops spatial thinking. And if you understand the laws on which the Space itself is built, it will be easier to understand other, much more interesting things that work in this space.

## General case

But back to our triangles. To begin with, we abstract away from particulars and see how to find the base of a triangle that is neither equilateral, nor isosceles, nor rectangular. Since either side can serve as a base in such a figure, first we will choose some sort of a side and “base” its base. Accordingly, turn the triangle so that it stands on it, and we will look for its length.

This will help us the famous cosine theorem, a special case of which is the Pythagorean theorem. The cosine theorem says that the square of one of the sides of a triangle is equal to the sum of the two other sides of the triangle, previously squared, minus the product of these sides multiplied by two and multiplied by the cosine of the angle between them.If the length of the two sides and the angle between them is known, then we substitute them into the formula and the problem is solved. If the data is different from this, then it is necessary to lower the height to the base, getting two right triangles. Well, how to find the base of a right triangle is a trivial task. The aspect ratio and angle allow you to calculate the length of the base with minimal data. Since the tasks in the textbook by definition must be solved, everything will turn out.

## Isosceles triangle

Simplify the task. In some tasks, the triangle is defined as isosceles. Recall isosceles is called a triangle that has two equal sides. The basis will be considered as the third party. How to find the base of an isosceles triangle in this case? It will be necessary to know one of the sides and the angle opposite to the base. Since the thighs are equal - the second side is known and equal to the first. And then, by the cosine theorem, we still find the base.

## Right triangle

A fairy tale for the student. Rectangular, it is a triangle with an angle of ninety degrees - the most convenient triangle. How to find the length of the base of a triangle with a right angle is a question that helps to find the aspect ratio in other, non-rectangular triangles.Other tasks often reduce to this by holding a height in a triangle, which breaks the figure into two right-angled triangles. Here a particular case of the cosine theorem, the Pythagorean theorem, comes into force. Since the cosine of a right angle is zero, the product of the sides vanishes, leaving only the sum of the squares of the legs on the right, while the left side of the equality is the square of the hypotenuse, the side opposite the right angle. And accordingly, the base of a right triangle can be considered any of its legs.

## Equilateral triangle

How to find the base of an equilateral triangle is an unusual question, generally speaking. To solve this "difficult" problem, you need to know the length of at least one side of the triangle. And since all sides of the triangle are equal (it is equilateral), the base will be equal to the length of the side. This problem is more for quick-wittedness than knowledge of geometry.