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

| July 29, 2021 | education

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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