From a point outside the plane, two inclined ones are drawn to it, each of which forms an angle of 45 with the plane

From a point outside the plane, two inclined ones are drawn to it, each of which forms an angle of 45 with the plane.determine the distance from this point to this plane if the angle between the inclined ones is 60 and the distance between the ends of the inclined ones is 10 cm.

From point A, let us drop the perpendicular to the plane α.

Consider two right-angled triangles AOC and AOB, in which the angles at the vertex O are right, and the angles at the vertices B and C are equal to 45, then the angles at the vertex A are equal to 45. Consequently, the triangles AOB and AOC are isosceles and AO = CO = BO. Then the hypotenuses AC and AB are also equal.

If AB = AC, then triangle ABC is isosceles with angle A equal to 60.

If in an isosceles triangle one of the angles is 60 degrees, then this triangle is equilateral, then AB = BC = AC = 10 cm.

Consider a right-angled, isosceles triangle AOS, determine the size of the AO leg.

SinC = AO / AC.

AO = Sin45 * 10 = 10 * √2 / 2 = 5 * √2 cm.

Answer: The distance from point A to the plane is 5 * √2 cm.