From a point to a plane, inclined ones are drawn, one of them has a projection of 3√2 and is inclined

| February 26, 2021 | education

From a point to a plane, inclined ones are drawn, one of them has a projection of 3√2 and is inclined to the plane at an angle of 45 degrees, the projection of the second inclined is equal to the root of 46. Find the distance between the bases of the inclined ones if the angle between the inclined ones is 60 degrees

In the right-angled triangle AOB, the angle OAB = 45, then the triangle AOB is isosceles, OB = AO = 3 * √2 cm.

By the Pythagorean theorem AB ^ 2 = AO ^ 2 + OB ^ 2 = 18 +18 = 36. AB = 6 cm.

In a right-angled triangle OBC, according to the Pythagorean theorem, BC ^ 2 = OB ^ 2 + OC ^ 2 = 18 + 46 = 64. BC = 8 cm.

In the triangle ABC, by the cosine theorem, we define the length of the groove AC.

AC ^ 2 = AB ^ 2 + BC ^ 2 – 2 * AB * BC * Cos60 = 36 + 64 – 2 * 6 * 8 * 1/2 = 100 – 48 = 52.

AC = 2 * √13 cm.

Answer: Between the bases of the inclined 2 * √13 cm.



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