To solve many geometric problems need to find the height of a given shape.These problems have practical value.During the determination of the height of construction work helps calculate the necessary amount of material and to determine how well made slopes and openings.Often the patterns required to build an understanding of the properties of geometric shapes.
Many people, despite good grades in school, in the construction of conventional geometric figures raises the question of how to find the height of a triangle or a parallelogram.Moreover, determination of the height of the triangle is the most challenging.This is because that the triangle can be acute, obtuse isosceles or rectangular.For each of the types of triangles have their own rules of construction and settlement.
How to find the height of the triangle in which all angles are acute, graphically
If all angles of a triangle acute (each corner of the triangle is less than 90 degrees), then to find the height you need to do the following.
- the specified parameters builds the triangle.
- following notation.A, B and C are vertices of the figure.The angles corresponding to each vertex - α, β, γ.Opposite corners of this side - a, b, c.
- height called the perpendicular dropped from the vertex to the opposite side of the triangle.To determine the height of the triangle we construct perpendiculars: from the vertex of the angle α to the side a, angle β from the top to the side b, and so on.
- point of intersection of height and sides a denoted H1, and the very height h1.The point of intersection of height and side b is H2, respectively height h2.For the side c is height h3, and the point of intersection of the H3.
Next to each type of triangle will use the same notation sides, angles, heights and vertices of triangles.
height of the triangle with an obtuse angle
now look at how to find the height of a triangle if one angle is obtuse (greater than 90 degrees).In this case, the height drawn from the obtuse angle will be inside the triangle.The other two height will be outside the triangle.
Let our triangle, the angles α and β are sharp, and the angle γ - dull.Then for building heights, coming out of the corners α and β, it is necessary to continue opposing sides of the triangle to a perpendicular.
How to find the height of the isosceles triangle
In this figure, there are two equal sides and bottom, with angles that are at the base, they are also equal to each other.This equality of the parties and facilitates the construction of corners and elevation calculation.
First draw a triangle itself.Let side b, and c, and the angles β, γ are respectively equal.
now hold the height of the vertex of the angle α, which we denote by h1.For this height of an isosceles triangle will be both a median and bisector.
Next construct two other height: h2 for the side b, and angle β, h3 for the side c and the angle γ.These heights are equal in length.
To make the base, only one construction.For example, the median of conduct - segment connecting the vertex of an isosceles triangle and the opposite side, a base for finding the altitude and bisector.And to calculate the length of the height of the other two parties can be built only one height.Thus, to graphically determine how to calculate the height of the isosceles triangle, a height sufficient to find two of the three.
How to find the height of a right triangle
have to determine the height of a right triangle is much easier than the others.This is because they themselves legs are at right angles, so are the heights.
To construct the third height, as usual, the perpendicular joining the vertex of the right angle and the opposite direction.As a result, in order to know how to find the height of the triangle in this case, it requires only one building.
