Perpendiculars MO = 8 cm and inclined 10 cm are drawn to the plane through point M. Find the inclined projection.

By condition, the MO is perpendicular to the plane α. The segment AO is the projection of the inclined AM on the plane α, then AO is perpendicular to the OM, and therefore the triangle AOM is rectangular.
In a right-angled triangle AOM, according to the Pythagorean theorem, AO ^ 2 = AM ^ 2 – OM ^ 2 = 100 – 64 = 36.
AO = 6 cm.
Answer: The projection length is 6 cm.