In a triangle CDE CD = 1, DE = 2√6, EC = 5. Find the height drawn from the vertex of the largest angle of the triangle.

The largest angle lies against the largest side, so we draw the DH height to the EC side.
We denote CH = X, HD = Y and compose two equations according to the Pythagorean theorem.
X ^ + Y ^ = 1 or Y ^ = 1 – X ^
(5 – X) ^ + Y ^ = 24
(5 – X) ^ + 1 – X ^ = 24
25 – 10 * X + X ^ + 1 – X ^ = 24
-10 * X = -2
X = 0.2
Y ^ = 1 – 0.04 = 0.96
Y = √ (0.96)
Answer: √ (0.96).