For what calculations does the height of an isosceles triangle

The triangle is one of the main figures in geometry. It is customary to select triangles straight (one angle at which is 90 ⁰ ), acute and obtuse (angles less than or greater than 90 ^0, respectively), equilateral and isosceles. In calculations of various kinds, the basic geometric concepts and quantities (sine, median, radius, perpendicular, etc.)

The theme for our study will be the height of an isosceles triangle. Deeper into terminology and definitions we will not, just briefly denote the basic concepts that will be needed to understand the essence.

Thus, an isosceles triangle is usually considered to be a triangle in which the magnitude of the two sides is expressed by the same number (equality of sides). An isosceles triangle can be both acute-angled, obtuse, and straight. It can also be equilateral (all sides of the figure are equal in size). Quite often you can hear: all equilateral triangles are isosceles, but not all isosceles are equilateral.

The height of any triangle is considered to be a perpendicular dropped from the corner to the opposite side of the figure. A median is a segment drawn from the corner of the figure to the center of the opposite side.

What is remarkable about the height of an isosceles triangle?

• If the height dropped on one side is a median and a bisector, then this triangle will be considered isosceles, and vice versa: the triangle is isosceles if the height dropped on one side is both a bisector and a median. This height is called the main one.
• The heights dropped on the side (equal) sides of an isosceles triangle are identical and form two similar figures.
• If the height of an isosceles triangle is known (as, indeed, any other), and the side to which this height was lowered, one can know the area of a given polygon. S = 1/2 * (c * h _c )

How is the height of an isosceles triangle used in calculations? Its properties, conducted to its foundation, make the following statements true:

• The main height, being simultaneously a median, divides the base into two equal segments. This allows us to know the size of the base, the area of the triangle formed by the height, etc.
• As a perpendicular, the height of an isosceles triangle can be considered the side (cate- tate) of a new rectangular triangle. Knowing the value of each side, based on the Pythagorean theorem (all known ratios of the squares of the legs and hypotenuse), one can calculate the numerical value of the height.

What is the height of the triangle? In general, an isosceles triangle, the height of which we need, does not cease to be so in its essence. Therefore, for him, all the formulas used for these figures, as such, do not lose their relevance. You can calculate the length of the height, knowing the size of the angles and sides, the size of the sides, the area and side, and a number of other parameters. The height of a triangle is equal to a certain ratio of these quantities. To bring the formula itself does not make sense, it is easy to find them. In addition, having a minimum of information, you can find the desired values and then proceed to calculate the height.