+452 In triangle ABC, angle ACB = 90 degrees. Let H be the foot of the altitude from C to side AB.
If BC = 1 and AH = 2, find CH.
+10 Explanation:
Triangle ABC is a right triangle with ∠ACB = 90°. The altitude CH creates two right triangles, AHC and BHC.
Using the Pythagorean theorem:
AC² = AH² + CH² → 4 + h²
BC² = BH² + CH² → 1 = b² + h², where b = AB - 2
From the area relation:
(2 + sqrt(1 - h²)) × h = 2
Solving for h, we get h = 1.
Thus, the final answer for CH is 1.
