The point is inside of an equilateral triangle with side length so that the distance from to two of the sides are and . Find the distance from to the third side.
the area of the equilateral triangle is immediately known. call the vertices of the equilateral triangle as A.B,C and join P to A,B and C. the triangle is subdivided into three sub-triangles out of which the area of two of the sub-triangles is known since the length of the altitudes are known. the third unknown one can be known by equating the area of the equilateral to the sum of the areas of the three sub-triangles.