From a point taken outside the plane, a perpendicular and two oblique ones are drawn. The length of one

| August 9, 2021 | education

From a point taken outside the plane, a perpendicular and two oblique ones are drawn. The length of one of them is exactly 25 cm, and the other is 24 cm. The second oblique forms an angle of 30 degrees with its projection. Find the length of the projection of the first oblique.

Consider a right-angled triangle ABO, in which the angle O is straight, since AO is perpendicular to the plane, and the angle B = 300 by condition. Then the leg AO lies opposite an angle of 300 and is equal to half of the hypotenuse AB. AO = AB / 2 = 24/2 = 12 cm.

The AOS triangle is also rectangular, then, according to the Pythagorean theorem, we find the length of the leg OS, which is the projection of the inclined AC on the plane.

OC ^ 2 = AC ^ 2 – AO ^ 2 = 25 ^ 2 – 12 ^ 2 – 625 – 144 = 481.

OS = √481 cm.

Answer: The length of the projection of the first oblique is √481 cm.



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