From that we have to calculate the slope of the perpendicular line through D. Now we need to determine the slope of BC. Slope of the altitude BE = -1/ slope of ACĮquation of the altitude BE is given as : From that we have to find the slope of the perpendicular line through B. We will solve an example to understand the correct use of formulae in finding the orthocenter.įind the coordinates of the orthocenter of a triangle whose vertices are (2, -3) (8, -2) and (8, 6).
How to Find the Orthocenter of a Triangle? Using an orthocenter calculator creates easiness in determining the coordinates of the orthocenter for any triangle. We need to determine the equation of the altitudes by using the expression as follows:Īfter this, we need to solve the algebraic equations to find values corresponding to x and y that are the coordinates of the orthocenter. Perpendicular slope of line = −1/slope of the line
The slope of all the sides is calculated by using the following formula:īy means of the formula below, we can determine the slope of the perpendicular drawn on each side of the triangle. We will discuss all basic formulae used in finding the orthocenter of a triangle. Algebraic Formulae to Calculate Orthocenter: The orthocenter calculator determines the orthocenter of any one of the triangles mentioned above. For this triangle, the orthocenter always lies outside the triangle.įor a right-angled triangle, the orthocenter lies on its vertex. The measure of one angle(obtuse angle) in an obtuse triangle is greater than 90°.
You can determine the orthocenter coordinates by using free online orthocenter calculator. In general, the orthocenter of an acute-angled triangle lies inside the triangle. Let us have a focus on some of the significant properties of the orthocenter.Īn acute triangle is the one that has all three angles (acute angles) less than 90°. When all right bisectors of a triangle intersect each other at a common point, that point has its own coordinates that are related to the coordinates of all the three vertices of the triangle.Īn orthocenter finder generates the absolute values of these coordinates within seconds. In the above figure, AB, BC and CA are the sides of the triangle and their respective altitudes are CF, AD and BE.Īn altitude is simply a perpendicular line (a line drawn at 90 degree angle) that is drawn from any vertex of the triangle to its opposite side. “ A point where the altitudes of the triangle meet is known as the point of concurrency or simply the orthocenter of the triangle.” Let us discuss the proper concept of the orthocenter in trigonometry. This tool results in exact values of the coordinates of the orthocenter. This formula is known as Heron's formula.An online Orthocenter calculator helps you to calculate the orthocenter of a triangle easily.
Altitude of a Triangle Formula for Scalene TriangleĪltitude of a scalene triangle is given as: \(h_a = \dfrac\), where a,b,c are the sides of the scalene triangle, and s is the semi perimeter. Let us learn different altitude formulas on various different conditions for different types of triangles. We know that triangles are classified on the basis of sides and angles. General Formula for Altitude of a Triangle (h) = (2 × Area) ÷ baseĪltitude of A Triangle Formula for Different Triangles Further, we can also see below the different altitudes of triangle formulas for different triangles. Here the altitude is represented by the alphabet h.
The altitude of a triangle formula can be expressed as follows. What Is the Altitude of A Triangle Formula? The altitude is used for the calculation of the area of a triangle. The altitude of a triangle formula is interpreted and different formulas are given for different types of triangles. The altitude of a triangle formula gives us the height of the triangle. The perpendicular drawn from the vertex to the opposite side of the triangle is called the altitude of a triangle.