In a right-angled triangle ABC, the height CD is drawn from the vertex of the right angle. AC: CB = 2: 3 and DB = 18. Find CD.
Since in a right-angled triangle, by condition, ABC AC / BC = 2/3, then tgABC = AC / BC = 2/3.
The segment CD is the height of the triangle BCD, then the triangle BCD is rectangular.
tgCBD = tgABC = 2/3.
tgCBD = CD / BD.
2/3 = CD / 18.
СD = 18 * 2/3 = 12 cm.
Answer: The length of the height CD is 12 cm.
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