From a point taken outside the plane, two inclined ones are drawn. the length of each inclined 6 cm.

| February 8, 2021 | education

From a point taken outside the plane, two inclined ones are drawn. the length of each inclined 6 cm. the angle between the inclined 60 degrees and the angle between their projections is a straight line. find the distance from point to plane

Consider a triangle ABC, which, by condition, has a side AB = AC = 6 cm, therefore the triangle is isosceles, and since the angle A = 60, it is equilateral, and then BC = AB = AC = 6 cm.

Since AB = AC, their projections onto the plane are also equal, OC = OB, and the angle between them, by condition, is straight.

Let OB = OC = X cm, then, by the Pythagorean theorem, BC ^ 2 = OB ^ 2 + OS ^ 2 = 2 * X ^ 2.

2 * X ^ 2 = 36.

X ^ 2 = 18.

X = 3 * √2.

ОВ = ОВ = 3 * √2.

The AOC triangle is rectangular, since AO is perpendicular to the plane, then, according to the Pythagorean theorem, AO ^ 2 = AC ^ 2 – OC ^ 2.

OA ^ 2 = 6 ^ 2 – (3 * √2) ^ 2 = 36 – 18 = 18.

ОА = √18 = 3 * √2 cm.

Answer: The length of the segment OA = 3 * √2 cm.



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