Triangle ABC, with a rectangular angle C, rests on the plane m and forms an angle with it = 45 degrees.

Triangle ABC, with a rectangular angle C, rests on the plane m and forms an angle with it = 45 degrees. leg AC = 2 m, hypotenuse AB: BC = 3: 1. Find the distance from the vertex B to the plane.

Let the length of the leg BC = X cm, then the length of the hypotenuse AB = 3 * X cm.

By the Pythagorean theorem, AB ^ 2 = BC ^ 2 + AC ^ 2.

9 * X ^ 2 = X ^ 2 + 4.

8 * X ^ 2 = 4.

X = BC = √2 / 2 cm.

Let’s construct a perpendicular BH. CH is the projection of the BC leg onto the plane, then the BCH angle, by condition, is 45.

Then BH = BC * Sin45 = (√2 / 2) * (√2 / 2) = 1/2 m.

Answer: From point B to plane 0.5 m.