Triangle Altitude Calculator
Calculate the lengths of all three altitudes of a triangle
Enter Vertex Coordinates
Altitude from A to BC (hₐ)
Altitude from B to AC (h_b)
Altitude from C to AB (h_c)
Triangle Properties:
Area = 0.000
Side a (BC) = 0.000
Side b (AC) = 0.000
Side c (AB) = 0.000
Visualization
About Triangle Altitudes
An altitude of a triangle is a perpendicular line segment from a vertex to the line containing the opposite side. Every triangle has three altitudes, and they all intersect at a single point called the orthocenter.
Key Properties
- All three altitudes intersect at the orthocenter
- An altitude is always perpendicular to the opposite side (or its extension)
- The altitude can fall outside the triangle for obtuse triangles
- In a right triangle, two altitudes are the legs of the triangle
- Altitude length is used to calculate the area: Area = (base × height) / 2
Altitude Formula
hₐ = (2 × Area) / a
Where hₐ is the altitude to side a, and Area is the triangle's area.
Frequently Asked Questions
What is an altitude of a triangle?
An altitude is a perpendicular line segment from a vertex to the opposite side (or the line containing the opposite side). It represents the height of the triangle when that opposite side is considered the base.
How do you calculate the altitude length?
The altitude length can be calculated using the formula h = (2 × Area) / base, where Area is the triangle's area and base is the side to which the altitude is drawn.
Where do the altitudes meet?
All three altitudes meet at a single point called the orthocenter. For acute triangles, it's inside; for right triangles, it's at the right angle vertex; for obtuse triangles, it's outside.
What's the difference between altitude and median?
An altitude is perpendicular to a side and may not bisect it, while a median connects a vertex to the midpoint of the opposite side but is not necessarily perpendicular.
Can an altitude be outside the triangle?
Yes, in an obtuse triangle, two of the three altitudes lie outside the triangle. They are drawn to the extensions of the opposite sides rather than to the sides themselves.
Why are altitudes important?
Altitudes are essential for calculating triangle area, finding the orthocenter, and solving various geometry problems. They're used in construction, engineering, and computer graphics.
How is altitude related to triangle area?
The area of a triangle equals (base × altitude) / 2. This relationship allows you to calculate either the area or the altitude if you know the other values.
Do all triangles have three altitudes?
Yes, every triangle has exactly three altitudes, one from each vertex. These altitudes may be inside or outside the triangle depending on the triangle type.
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