altitude

01 Minimum distance between projection points on the legs of right triangle

Problem
From the right triangle ABC shown below, AB = 40 cm and BC = 30 cm. Points E and F are projections of point D from hypotenuse AC to the perpendicular legs AB and BC, respectively. How far is D from AB so that length EF is minimal?
 

030-projections-of-d.gif

 

The Regular Tetrahedron

Regular tetrahedron is one of the regular polyhedrons. It is a triangular pyramid whose faces are all equilateral triangles.
 

Regular Pyramid

A regular pyramid is one whose base is a regular polygon whose center coincides with the foot of the perpendicular dropped from the vertex to the base.
 

The Pyramid

A pyramid is a polyhedron with a polygon base of any shape, and all other faces are triangles which have common vertex.
 

The Right Circular Cylinder

A right circular cylinder is a cylinder whose base is a circle and whose elements are perpendicular to its base.
 

Properties of Triangle

Side
Side of a triangle is a line segment that connects two vertices. Triangle has three sides, it is denoted by a, b, and c in the figure below.
 

Vertex
Vertex is the point of intersection of two sides of triangle. The three vertices of the triangle are denoted by A, B, and C in the figure below. Notice that the opposite of vertex A is side a, opposite to vertex B is side B, and opposite to vertex C is side c.
 

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