BO – perpendicular to the plane BA and BC – inclined, ОА = 1/4 OC.

BO – perpendicular to the plane BA and BC – inclined, ОА = 1/4 OC. find the distance from point B to the plane if AB = 10 cm BC = 20 cm.

Let the length of the segment OA = X cm, then, by condition, the length of the segment OC = 4 * X cm.

In the right-angled triangles BOA and BOC, according to the Pythagorean theorem, we express the general leg BO.

ВO ^ 2 = BC ^ 2 – OС^ 2 = 400 – 16 * X ^ 2.

BO ^ 2 = BA ^ 2 = OA ^ 2 = 100 – X ^ 2.

Then: 400 – 16 * X ^ 2 = 100 – X ^ 2.

15 * X ^ 2 = 300.

X ^ 2 = 20.

X = OA = 2 * √5 cm.

Then ВO ^ 2 = 100 – 20 = 80.

ВO = 4 * √5 cm.

Answer: From point B to plane 4 * √5 cm.