In a right-angled triangle ABC, the BC leg is located opposite an angle of 30, then BC = AB / 2 = 80/2 = 40 cm.
Triangles ABC and BCH are rectangular, in which the angle at the vertex B is common, then the right-angled triangles ABC and BCH are similar in acute angle.
Then the angle CAB = BCH = 30.
In a right-angled triangle BCH, the BH leg lies opposite an angle of 30, then BH = BC / 2 = 40/2 = 20 cm.
Answer: The length of the segment BH is 20 cm.
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