# From point M, which is 10 cm away from the plane, an oblique is drawn, making an angle of 30 degrees with the plane

From point M, which is 10 cm away from the plane, an oblique is drawn, making an angle of 30 degrees with the plane. Find an inclined projection on a given plane.

Let MH be the distance from point M to the plane. MH perpendicular to the plane. MH = 10 cm.

Let MA be inclined to the plane, point A belongs to this plane. Angle MAH = 30 °. AH is the desired projection inclined to the plane.

Consider the triangle МАH: angle Н = 90 ° (since the segment АН is perpendicular to МН).

In a right-angled triangle opposite an angle of 30 ° lies a leg, half the size of the hypotenuse. Opposite the corner of the MAH is the leg MH = 10 cm, which means that the hypotenuse MA = 10 * 2 = 20 cm.

We calculate the length АH according to the Pythagorean theorem:

AH = √ (AM² – MH²) = √ (20² – 10²) = √ (400 – 100) = √300 = √ (100 * 3) = 10√3 cm.

Answer: the projection of the oblique is 10√3 cm.

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