Altitudes of a Triangle

kind of triangle	position of H
acute triangle	within the triangle
right triangle	on the corner of the right angle
obtuse triangle	outside the triangle

The following equations are valid for the relations between the altitudes, the angles and sides:

h_a = bsin γ = csin β
h_b = csin α = asin γ
h_c = asin β = bsin α

There are a two theorems concerning the altitudes of a triangle which can be used to construct triangles:

• The altitude of a triangle dissects the triangle into two right triangles. The base point of the altitude is always located on the two circles defined by Thales' Theorem.
   
• The lengths of the altitudes of a triangle are indirect proportional to the corresponding sides:
  h_a : h_b = b : a
  h_a : h_c = c : a
  h_b : h_c = c : b
  
  h_a : h_b : h_c = 1/a : 1/b : 1/c