How to find the height length in a triangle

A triangle is one of the most interesting figures in geometry. It has many properties and patterns. Today we will focus on finding the length of the height of the triangle - a perpendicular drawn from the top to the opposite side or to its continuation (this side is called the base of the triangle).

Instruction manual

one

Designate the height with the letter h, it drops to side a. It should be remembered that in different triangles the heights are expressed in different ways. In the obtuse, one of the heights is inside the triangle, and the rest fall on the continuation of two sides and are outside the figure. All heights lie inside in an acute-angled triangle. And in a rectangular leg, the heights are. It is also necessary to mention such a thing as an orthocenter. The orthocenter is the point at which all three heights invariably intersect. In different triangles it is in different places. In obtuse - outside the triangle. Inside the orthocenter is located exclusively in an acute-angled triangle. In a rectangular one, it coincides with a right angle.

2

Then find the number p by adding all sides and then dividing this amount in half. It turns out like this: p = 2 / (a ​​+ b + c). The value of p is sure to come in handy for subsequent actions, be careful when finding it.

3

Multiply pc by three differences. The number p itself will be reduced each time, and the same sides will be subtracted. It should turn out: p (pa) (pb) (pc).

4

From the result, extract the root and double the result. 2 ^ p (pa) (pb) (pc). At this stage of the calculations, a calculator is most likely indispensable. Getting a large root expression in this case is more likely, so don't be surprised.

5

Divide the last number by the base a. As a result, the action looks like this: h = (2 ^ (pa) (pb) (pc)) / a. Further operations depend on the value obtained. It may be necessary to remove something from under the root for a more accurate meaning. The result is ready.

note

Several formulas to find the length of the height of the triangle. Height - the perpendicular coming from any vertex of the triangle, to the opposite side (or its continuation, for a triangle with an obtuse angle).

Useful advice

Formulas for a triangle, how to find the side, bisector, median, height, angle … H - height from a right angle. a, b - legs. c - hypotenuse. c1, c2 - segments obtained from dividing the hypotenuse, by height. α, β - angles during hypotenuse. The formula for the length of the height across the sides, (H)