# From point to plane, a perpendicular and an inclined line are drawn, the length of which is 20 cm.

**From point to plane, a perpendicular and an inclined line are drawn, the length of which is 20 cm. The angle between the inclined and its projection is 60 degrees. Find the length of the perpendicular.**

To solve this problem, it is necessary to use the Pythagorean theorem. It is known that the angle between oblique and projection is 60 °. This means that the angle between the perpendicular and the oblique is 30 °. This means that the projection of the inclined onto the plane is half the hypotenuse. It is known that the square of an oblique is equal to the sum of the squares of the perpendicular and the projection of this oblique. Let’s denote the projection as x:

x * x + 400 = 4x * x;

Solving the quadratic equation, we get that the length of the perpendicular is 10 * root of 3.