We start with an obtuse triangle PQR.
See also the version for acute triangles.


1. Choose one side of the triangle and extend it in both directions.
This is done because the side may not be long enough to perform the steps that follow. 

In steps 2 through 5 which follow, we are constructing the perpendicular to the line PQ through R.
This is is the same construction as
Constructing a perpendicular to a line through an external point. 
2. Set the compass on the opposite vertex (here R) and set the width to beyond the line PQ. 

3. Make two arcs across PQ, creating the points A and B.


4. From A and B, make two arcs that overlap, creating point C.
Make sure both arcs are drawn with the same compass width.


5. Draw a line through R and C. Label the point S where it crosses PQ.


Done The segment RS is an altitude of the triangle PQR.

