Question

The cosine of the obtuse angle formed by the medians

Answer 1

What is the cosine of the obtuse angle formed from the intersection of the two medians drawn from the vertex of the acute angles of an isosceles right triangle? That's a mouthful but consider sketch below: Median CD, which perpendicularly bisects AB, has a 2 to 1 ratio from CO to OD. We need to find angle AOB.

Answer 2

What is the cosine of the obtuse angle formed from the intersection of the two medians drawn from the vertex of the acute angles of an isosceles right triangle? That's a mouthful but consider sketch below:



Median CD, which perpendicularly bisects AB, has a 2 to 1 ratio from CO to OD. We need to find angle AOB.

Tangent theta = 2/3 which means theta is 33.7 degrees. Angle DOB must be 90–33.7 = 56.3 deg.

Therefore angle AOB is 112.6 degrees.

Cosine 112.6 deg = -.384