How to find the height of a triangle?

First of all, a triangle is a geometricA figure that is formed by three points that do not lie on a single straight line, which are connected by three segments. To find out what the height of a triangle is equal to, it is necessary, first of all, to determine its type. Triangles differ in the magnitude of the angles and in the number of equal angles. By the magnitude of the angles, the triangle can be acute, obtuse and rectangular. By the number of equal parties, an isosceles, equilateral and versatile triangles are distinguished. The height is the perpendicular, which is lowered to the opposite side of the triangle from its vertex. How to find the height of a triangle?

How to find the height of an isosceles triangle

The isosceles triangle is characterized byequality of sides and angles at its base, therefore, the heights of an isosceles triangle drawn to the sides are always equal to each other. Also, the height of this triangle is also a median and a bisectrix. Accordingly, the height divides the base in half. We consider the resulting rectangular triangle and find the side, that is, the height of an isosceles triangle, by the Pythagorean theorem. Using the following formula, calculate the height: H = 1/2 * √4 * a2- b2, where: a is the side of this isosceles triangle, b is the base of this isosceles triangle.

How to find the height of an equilateral triangle

A triangle with equal sides is calledequilateral. The height of such a triangle is derived from the height formula of an isosceles triangle. It turns out: H = √3 / 2 * a, where a is the side of this equilateral triangle.

How to find the height of a versatile triangle

Versatile is the triangle, whichany two sides are not equal to each other. In such a triangle, all three heights will be different. The lengths can be calculated using the formula: H = sin60 * a = a * (sgrt3) / 2, where a is the side of the triangle or first calculate the area of ​​a particular triangle according to Heron's formula, which looks like: S = (p * (pc) * (pb) * (pa)) ^ 1/2, where a, b, c are sides of the versatile triangle, and p is its half -perimeter. Each height = 2 * area / side

How to find the height of a right triangle

A right triangle has one right angle. The height that passes to one of the legs is at the same time the second leg. Therefore, in order to find the heights lying on the legs, it is necessary to use the modified Pythagoras formula: a = √ (c2- b2), where a, b are the legs (a is the cathetus thatit is necessary to find), c - the length of the hypotenuse. In order to find the second height, we must put the resulting value of a in place b. To find the third inside the triangle, the following formula is used: h = 2s / a, where h is the height of the right triangle, s is its area, and a is the length of the side to which the height will be perpendicular.

The triangle is called acute in the case,if all its angles are sharp. In this case, all three heights are located inside the acute-angled triangle. A triangle is called obtuse with one obtuse angle. The two heights of the obtuse triangle are outside the triangle and fall on the continuation of the sides. The third side is inside the triangle. The height is determined by the same Pythagorean theorem.

General formulas, like calculating the height of a triangle

  • The formula for finding the height of the triangle through the sides: H = 2 / a √p * (pc) * (pb) * (pb), where h is the height to be found, and, b and c are the sides of the triangle, p is its semiperimeter,.
  • The formula for finding the height of a triangle through an angle and a side: H = b sin y = c sin ß
  • The formula for finding the height of the triangle in terms of area and side: h = 2S / a, where a is the side of the triangle, and h is the height to the side a.
  • The formula for finding the height of the triangle through the radius and sides: H = bc / 2R.

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