pohjakulmat

Pohjakulmat are the base angles of a triangle—the angles at the endpoints of the base side. In a triangle labeled ABC with BC chosen as the base, the pohjakulmat are the angles ∠B and ∠C.

In any triangle, the interior angles sum to 180 degrees, so ∠B + ∠C = 180° − ∠A. In an isosceles triangle where AB = AC, the base angles are equal: ∠B = ∠C. Consequently, each base angle equals (180° − ∠A)/2. If AB = AC = s and the base BC has length b, then in the right triangle formed by dropping a height to the base, cos ∠B = (b/2)/s, i.e. ∠B = arccos(b/(2s)). The height h satisfies h = sqrt(s^2 − (b/2)^2) and sin ∠B = h/s.

For a non-isosceles triangle, base angles can be found using the Law of Cosines: cos ∠B = (AB^2 + BC^2 − AC^2) / (2 · AB · BC) and cos ∠C = (AC^2 + BC^2 − AB^2) / (2 · AC · BC). In a right triangle, the two non‑right angles are the base angles and sum to 90 degrees.

Pohjakulmat are central in geometric problem solving and angle chasing, particularly in constructions involving isosceles triangles and base-side relations.