From point to plane, 2 oblique 17 and 10 cm long are drawn, the projections of which are 5: 2.

From point to plane, 2 oblique 17 and 10 cm long are drawn, the projections of which are 5: 2. Find the distance from the point to the plane.

The distance from a point to a plane is a perpendicular drawn from a given point to a plane. Therefore, we have two right-angled triangles, in which the oblique are the hypotenuses, the projections of the oblique are the legs, and the segment h drawn from a point to the plane is the leg common for the two triangles.

Oblique projections are related as 5: 2, so their lengths can be designated as 5x and 2x.

According to the Pythagorean theorem, the square of the leg can be found as the difference between the squares of the hypotenuse and the second leg.

This means that for a larger triangle we can write: h2 = 17 ^ 2 – (5x) ^ 2 = 289 – 25x ^ 2;

For a smaller triangle: h ^ 2 = 10 ^ 2 – (2x) ^ 2 = 100 – 4x ^ 2;

Hence, 289 – 25x ^ 2 = 100 – 4x ^ 2;

21x ^ 2 = 189;

x ^ 2 = 189/21 = 9 = 32;

x = 3, which means that the projection of an oblique equal to 10 cm is 2 * 3 = 6 cm, and the projection of an oblique equal to 17 cm is 5 * 3 = 15 cm.

h ^ 2 = 10 ^ 2 – 6 ^ 2 = 100 – 36 = 64;

h = √64 = 8 cm – the required distance from a point to a plane.